PM Review — Lines and Angles

Question 1 Difficulty 1

What type of angle is less than 90 degrees?

A Right Angle
B Obtuse Angle
C Acute Angle
D Straight Angle

💡 Explanation An acute angle is defined as being less than 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 2 Difficulty 1

What is a straight angle?

A More than 90 degrees
B Exactly 90 degrees
C Exactly 180 degrees
D Less than 90 degrees

💡 Explanation A straight angle measures exactly 180 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 3 Difficulty 1

Which of the following is a right angle?

A 45 degrees
B 90 degrees
C 120 degrees
D 180 degrees

💡 Explanation A right angle is defined as measuring exactly 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 4 Difficulty 1

How many degrees are in a complete angle?

A 360 degrees
B 180 degrees
C 90 degrees
D 270 degrees

💡 Explanation A complete angle measures 360 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 5 Difficulty 1

Which of the following angles is obtuse?

A 30 degrees
B 90 degrees
C 150 degrees
D 180 degrees

💡 Explanation An obtuse angle is defined as being greater than 90 degrees but less than 180 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 6 Difficulty 1

What type of angle is exactly 90 degrees?

A Acute Angle
B Right Angle
C Obtuse Angle
D Straight Angle

💡 Explanation A right angle is defined as being exactly 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 7 Difficulty 1

If two lines intersect, what do they form?

A Angles
B Circles
C Triangles
D Squares

💡 Explanation When two lines intersect, they form angles at the point of intersection.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 8 Difficulty 1

Which angle is greater than 90 degrees but less than 180 degrees?

A Acute Angle
B Right Angle
C Obtuse Angle
D Straight Angle

💡 Explanation An obtuse angle is defined as being between 90 and 180 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 9 Difficulty 1

Which of the following is NOT a type of angle?

A Acute Angle
B Right Angle
C Obtuse Angle
D Sharp Angle

💡 Explanation Sharp angle is not a standard term in geometry; the correct terms are acute, right, and obtuse.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 10 Difficulty 1

What angle is formed by the hands of a clock at 3 o'clock?

A 90 degrees
B 180 degrees
C 270 degrees
D 360 degrees

💡 Explanation At 3 o'clock, the hands of the clock form a right angle, which is 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 11 Difficulty 2

If one angle is 70 degrees, what is the measurement of its complement?

A 20 degrees
B 30 degrees
C 90 degrees
D 110 degrees

💡 Explanation The complement of an angle is found by subtracting it from 90 degrees: 90 - 70 = 20 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 12 Difficulty 2

If two angles are supplementary and one is 110 degrees, what is the other angle?

A 70 degrees
B 80 degrees
C 90 degrees
D 100 degrees

💡 Explanation Supplementary angles add up to 180 degrees: 180 - 110 = 70 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 13 Difficulty 2

Which pair of angles are complementary?

A 60 degrees and 30 degrees
B 70 degrees and 110 degrees
C 50 degrees and 50 degrees
D 120 degrees and 60 degrees

💡 Explanation Complementary angles add up to 90 degrees: 60 + 30 = 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 14 Difficulty 2

If one angle is 45 degrees, what type of angle is its supplement?

A Acute Angle
B Right Angle
C Obtuse Angle
D Straight Angle

💡 Explanation The supplement of 45 degrees is 135 degrees, which is an obtuse angle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 15 Difficulty 2

Two angles are equal and they add up to 180 degrees. What type of angles are they?

A Acute Angles
B Right Angles
C Obtuse Angles
D Straight Angles

💡 Explanation If two angles are equal and add up to 180 degrees, they are straight angles.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 16 Difficulty 2

If a right angle is divided into two equal parts, what type of angles are formed?

A Acute Angles
B Right Angles
C Obtuse Angles
D Straight Angles

💡 Explanation Dividing a right angle (90 degrees) into two equal parts results in two 45-degree angles, which are acute.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 17 Difficulty 2

In a triangle, if one angle is 90 degrees, what is the type of the triangle?

A Acute Triangle
B Right Triangle
C Obtuse Triangle
D Equilateral Triangle

💡 Explanation A triangle with one angle measuring 90 degrees is classified as a right triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 18 Difficulty 2

What is the measure of an angle that is twice as large as its complement?

A 30 degrees
B 60 degrees
C 90 degrees
D 120 degrees

💡 Explanation Let the complement be x. Then the angle is 2x = 90 - x. Solving gives x = 30 degrees (complement) and the angle = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 19 Difficulty 2

What is the measure of an angle that is 30 degrees less than a right angle?

A 30 degrees
B 60 degrees
C 90 degrees
D 120 degrees

💡 Explanation A right angle is 90 degrees, so 90 - 30 = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 20 Difficulty 2

If two angles are complementary and one angle is 35 degrees, what is the other angle?

A 25 degrees
B 45 degrees
C 55 degrees
D 65 degrees

💡 Explanation The other angle is 90 - 35 = 55 degrees since they are complementary.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 21 Difficulty 3

In a quadrilateral, if three angles are 90 degrees each, what is the fourth angle?

A 90 degrees
B 180 degrees
C 270 degrees
D 360 degrees

💡 Explanation The sum of all angles in a quadrilateral is 360 degrees. Therefore, 360 - (90 + 90 + 90) = 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 22 Difficulty 3

If two angles are complementary and one angle is increased by 10 degrees, how many degrees is the other angle?

A Decrease by 10 degrees
B Remains the same
C Increase by 10 degrees
D Cannot be determined

💡 Explanation If one angle increases, the other angle must decrease by the same amount to remain complementary.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 23 Difficulty 3

If an angle measures 40 degrees, what is the measurement of its supplement and how does it relate to a straight angle?

A 140 degrees, 40 degrees less
B 140 degrees, 40 degrees more
C 50 degrees, 50 degrees less
D 90 degrees, 90 degrees more

💡 Explanation The supplement of 40 degrees is 140 degrees. It is 40 degrees less than a straight angle (180 degrees).

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 24 Difficulty 3

In a right triangle, if one angle is 30 degrees, what is the measure of the other angle?

A 30 degrees
B 60 degrees
C 90 degrees
D 120 degrees

💡 Explanation In a right triangle, the sum of angles is 180 degrees. Thus, the other angle is 90 - 30 = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 25 Difficulty 3

What is the measure of an angle that is 10 degrees less than twice its supplement?

A 30 degrees
B 40 degrees
C 50 degrees
D 60 degrees

💡 Explanation Let x be the angle. Then, x = 2(180 - x) - 10. Solving gives x = 50 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 26 Difficulty 3

If the sum of two angles is 150 degrees and one angle is 60 degrees, what is the other angle?

A 70 degrees
B 80 degrees
C 90 degrees
D 100 degrees

💡 Explanation To find the other angle: 150 - 60 = 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 27 Difficulty 3

If a triangle has angles measuring 50 degrees and 60 degrees, what is the measure of the third angle?

A 50 degrees
B 60 degrees
C 70 degrees
D 80 degrees

💡 Explanation The sum of angles in a triangle is 180 degrees. Therefore, 180 - (50 + 60) = 70 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 28 Difficulty 3

If two angles are equal and they add up to 120 degrees, what is the measure of each angle?

A 30 degrees
B 40 degrees
C 60 degrees
D 80 degrees

💡 Explanation If two angles are equal, each angle is 120/2 = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 29 Difficulty 3

What is the measure of an angle if it is three times its complement?

A 60 degrees
B 30 degrees
C 45 degrees
D 75 degrees

💡 Explanation Let x be the angle. Then x = 3(90 - x). Solving gives x = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 30 Difficulty 3

If the measure of an angle is 20 degrees more than its supplement, what is the measure of the angle?

A 50 degrees
B 60 degrees
C 70 degrees
D 80 degrees

💡 Explanation Let x be the angle. Then x = (180 - x) + 20. Solving gives x = 70 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 31 Difficulty 4

In a parallelogram, if one angle is 70 degrees, what are the measures of the other three angles?

A 70, 70, 110 degrees
B 70, 110, 70 degrees
C 70, 70, 110 degrees
D 70, 70, 80 degrees

💡 Explanation In a parallelogram, opposite angles are equal, and adjacent angles are supplementary. Thus, if one angle is 70 degrees, the other three angles are 70, 110, and 70 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 32 Difficulty 4

If two angles are in the ratio 2:3 and their sum is 90 degrees, what are the angles?

A 30, 60 degrees
B 20, 70 degrees
C 40, 50 degrees
D 10, 80 degrees

💡 Explanation Let the angles be 2x and 3x. Then, 2x + 3x = 90 degrees. Solving gives x = 18 degrees, resulting in angles of 30 degrees and 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 33 Difficulty 4

What is the measure of an angle that is 40 degrees more than half of its supplement?

A 70 degrees
B 80 degrees
C 90 degrees
D 100 degrees

💡 Explanation Let x be the angle. Then, x = 40 + 0.5(180 - x). Solving gives x = 80 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 34 Difficulty 4

If the exterior angle of a triangle is 120 degrees, what is the measure of the opposite interior angle?

A 40 degrees
B 60 degrees
C 80 degrees
D 90 degrees

💡 Explanation The exterior angle of a triangle is equal to the sum of the two opposite interior angles. If one of them is known, the other can be calculated.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 35 Difficulty 4

In a right triangle, if one angle is 45 degrees, what is the measure of the other angle in relation to the triangle's properties?

A 30 degrees
B 45 degrees
C 60 degrees
D 90 degrees

💡 Explanation In a right triangle, the angles must sum to 180 degrees. If one angle is 45 degrees, the other angle must also be 45 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 36 Difficulty 4

If two angles are supplementary and one angle is three times the other, what are the angles?

A 30, 150 degrees
B 45, 135 degrees
C 60, 120 degrees
D 75, 105 degrees

💡 Explanation Let one angle be x. Then, the other angle is 3x. Setting up the equation x + 3x = 180 degrees gives x = 45 degrees, making the angles 60 and 120 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 37 Difficulty 4

If an angle is bisected and the resulting angles are in a ratio of 1:2, what is the measure of the original angle?

A 60 degrees
B 90 degrees
C 120 degrees
D 150 degrees

💡 Explanation Let the original angle be x. The two bisected angles would be x/3 and 2x/3, which add up to x. Setting up the equation gives x = 120 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 38 Difficulty 4

If the angles of a triangle are in the ratio 3:4:5, what are the measures of the angles?

A 30, 40, 50 degrees
B 36, 48, 60 degrees
C 45, 60, 75 degrees
D 54, 72, 90 degrees

💡 Explanation Let the angles be 3x, 4x, and 5x. The sum of angles in a triangle is 180 degrees, leading to x = 180/12 = 15 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 39 Difficulty 4

If an angle is 20 degrees less than twice its complement, what is the measure of the angle?

A 40 degrees
B 50 degrees
C 60 degrees
D 70 degrees

💡 Explanation Let the angle be x. Then, x = 2(90 - x) - 20. Solving gives x = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 40 Difficulty 4

In a circle, if an angle is formed by two radii, what is the relationship between the angle and the arc it subtends?

A The angle is half the arc
B The angle is equal to the arc
C The angle is twice the arc
D No relationship

💡 Explanation The angle formed at the center of a circle by two radii is equal to the arc it subtends.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?