Lines and Angles

Solved Questions on Lines and Angles

1. If ∠ AOB and ∠ COD are vertically opposite angles, and the measure of ∠ AOB is 40°, what is the measure of a ∠ COD?

a) 40°
b) 50°
c) 80°
d) 140°

Answer: a) 40°

Explanation: Vertically opposite angles are equal in measure, so if the measure of ∠ AOB is 40°, then the measure of ∠ COD is also 40°.

2. An angle and its complement have a sum that is twice the measure of the complement. What is the measure of the angle?

a) 45°
b) 54°
c) 72°
d) 108°

Answer: a) 45°

Explanation: Let x be the measure of the complement, then the angle measures (90 – x)°. The problem states that the sum of the angle and its complement is twice the measure of the complement, so we can write:
(90 – x) + x = 2x
2x = 90
x = 45°
Solving for x, we get x = 45°.

Therefore, the angle measures 90^o – 45^o = 45^o.

3. If one angle in a pair of supplementary angles is 75°, what is the measure of the other angle?

a) 75°
b) 105°
c) 115°
d) 135°

Answer: d) 105°

Explanation: Since the pair of angles are supplementary, their sum is 180°. So, if one angle is 75°, the other angle must be 180o - 75o = 105°.

4. If two parallel lines are intersected by a transversal and the measure of one of the exterior angles formed is 150°, what is the measure of the corresponding interior angle on the same side of the transversal?

a) 30°
b) 60°
c) 120°
d) 150°

Answer: a) 30°

Explanation: The exterior angle and the corresponding interior angle are supplementary, which means the sum of their measures is 180^o.

So, the measure of the corresponding interior angle is 180^o - 150^o = 30°

5. In triangle PQR, the measure of ∠ P is 40° and the measure of ∠ R is 70°. What is the measure of exterior angle ∠ Q?

a) 40°
b) 90°
c) 100°
d) 110°

Answer: d) 110°

Explanation: The angle ∠ Q is an exterior angle of ? PQR and according to the exterior angle property, it is equal to the sum of the measures of ∠ P and ∠ R.

Thus, ∠ Q = ∠ P + ∠ R. Substituting the given values, we get ∠ Q = 40 + 70 = 110°.

Practice Questions on Lines and Angles

1. If the measure of one angle in a pair of vertically opposite angles is 75°, what is the measure of the other angle?

a) 75°
b) 90°
c) 105°
d) 180°

Answer: a) 75°

2. If the measure of an angle is 10° less than its complement, what is the measure of the larger angle?

a) 15°
b) 30°
c) 45°
d) 50°

Answer: d) 50°

3. What is the definition of supplementary angles?

a) Two angles whose sum is 90°
b) Two angles whose sum is 180°
c) Two angles whose sum is 270°
d) Two angles whose sum is 360°

Answer: b) Two angles whose sum is 180°

4. If two parallel lines are intersected by a transversal, and the measure of one of the interior angles formed is 110°, what is the measure of its corresponding angle?

a) b) 70°
b) 90°
c) 110°
d) 120°

Answer: a) 110°

5. What is the name of an angle that measures greater than 90° but less than 180°?

a) Right angle
b) Obtuse angle
c) Acute angle
d) Straight angle

Answer: b) Obtuse angle

6. Two parallel lines are intersected by a transversal and the measure of one of the exterior angles formed is 130°. What is the measure of the angle that is supplementary to this angle?

a) 50°
b) 70°
c) 110°
d) 150°

Answer: a) 50°

7. If two parallel lines are intersected by a transversal and the measure of one of the interior angles formed is 60°, what is the measure of the exterior angle adjacent to it?

a) 30°
b) 60°
c) 120°
d) 150°

Answer: c) 120°

8. What is the name of an angle that measures exactly 90°?

a) Right angle
b) Obtuse angle
c) Acute angle
d) Straight angle

Answer: a) Right angle

9. What is the name of a line that has a beginning point but no end point?

a) Ray
b) Line segment
c) Line
d) Infinity line

Answer: a) Ray

10. What is the name of an angle that measures exactly 360 degrees?

a) Right angle
b) Obtuse angle
c) Acute angle
d) Complete angle

Answer: d) Complete angle