Question 1

Three lines meet at a point. If two of the angles formed are 85° and 120°, what is the measure of the third angle?

Accepted Answer

Step 1: When three lines meet at a point, all angles around that point sum to 360°. Step 2: Third angle = 360° − 85° − 120° = 155°. Therefore, the answer is 155°.

Question 2

A line makes an angle of 48° with the horizontal. What is the angle it makes with the vertical?

Accepted Answer

Step 1: The angle between a line and the horizontal, plus the angle between the same line and the vertical, equals 90° (they are complementary). Step 2: Angle with vertical = 90° − 48° = 42°. Therefore, the answer is 42°.

Question 3

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 73°, what is the measure of the other alternate interior angle?

Accepted Answer

Step 1: When a transversal cuts two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 73°, the other alternate interior angle is also 73°. Therefore, the answer is 73°.

Question 4

A transversal intersects two parallel lines. If a corresponding angle is 56°, what is the measure of the co-interior angle on the same side of the transversal?

Accepted Answer

Step 1: Corresponding angles are equal when a transversal cuts parallel lines. Step 2: Co-interior angles (also called consecutive interior angles) are supplementary, summing to 180°. Step 3: If the corresponding angle is 56°, the co-interior angle on the same side = 180° − 56° = 124°. Therefore, the answer is 124°.

Question 5

At an intersection, four angles are formed. If the largest angle is 138°, what is the measure of the smallest angle?

Accepted Answer

Step 1: When two lines intersect, they form two pairs of vertically opposite angles. Step 2: Adjacent angles are supplementary (sum to 180°). Step 3: If the largest angle is 138°, the adjacent angle (smallest) = 180° − 138° = 42°. Step 4: The other two angles are vertically opposite to these, so they are also 138° and 42°. Therefore, the smallest angle is 42°.

Question 6

Two lines intersect at a point. If one of the angles formed is 65°, what is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (sum to 180°). Step 2: If one angle is 65°, the adjacent angle = 180° − 65° = 115°. Therefore, the answer is 115°.

Question 7

In a triangle, one angle is twice the second angle, and the third angle is 30° less than the second angle. What is the measure of the largest angle in the triangle?

Accepted Answer

Step 1: Let the second angle be x. Then the first angle = 2x, and the third angle = x − 30°. Step 2: Sum of angles in a triangle = 180°. So: 2x + x + (x − 30°) = 180°. Step 3: 4x − 30° = 180° → 4x = 210° → x = 52.5°. Step 4: The three angles are 2x = 105°, x = 52.5°, and x − 30° = 22.5°. Step 5: The largest angle = 105°.

Question 8

A line makes an angle of 35° with the positive x-axis. What is the angle that the same line makes with the negative x-axis?

Accepted Answer

Step 1: The positive x-axis and negative x-axis are opposite rays on the same line, forming a straight angle of 180°. Step 2: If a line makes an angle of 35° with the positive x-axis, the angle it makes with the negative x-axis = 180° − 35° = 145°. Step 3: Therefore, the answer is 145°.

Question 9

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the sum of the two co-interior angles (also called consecutive interior angles) on the same side of the transversal?

Accepted Answer

Step 1: When a transversal intersects two parallel lines, alternate interior angles are equal. So the other alternate interior angle = 72°. Step 2: Co-interior angles (consecutive interior angles on the same side) are supplementary, meaning they sum to 180°. Step 3: Therefore, the sum of the two co-interior angles = 180°.

Question 10

Two lines intersect at a point. One of the angles formed is 65°. What is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (sum to 180°). Step 2: If one angle is 65°, the adjacent angle = 180° − 65° = 115°. Therefore, the answer is 115°.

Question 11

In a triangle, the exterior angle at one vertex is 110°. If the two non-adjacent interior angles are in the ratio 3:2, what is the measure of the larger of these two non-adjacent interior angles?

Accepted Answer

Step 1: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. So the sum of the two non-adjacent angles = 110°. Step 2: Let the angles be 3x and 2x. Then 3x + 2x = 110°, so 5x = 110°, giving x = 22°. Step 3: The larger angle = 3x = 3 × 22° = 66°.

Question 12

In triangle PQR, angle P = 50° and angle Q = 60°. A line is drawn from vertex R perpendicular to side PQ, meeting PQ at point M. What is the measure of angle PRM (in degrees)?

Accepted Answer

Step 1: Find angle R in triangle PQR: angle R = 180° - 50° - 60° = 70°. Step 2: In triangle PRM, angle P = 50° and angle M = 90° (since RM is perpendicular to PQ). Step 3: Using angle sum in triangle PRM: angle P + angle M + angle PRM = 180°. Step 4: 50° + 90° + angle PRM = 180°, so angle PRM = 40°.

Question 13

In triangle ABC, angle A = 45° and angle B = 75°. The exterior angle at C is bisected by a line. What is the measure of the angle between this bisector and side BC (in degrees)?

Accepted Answer

Step 1: Find angle C: angle C = 180° - 45° - 75° = 60°. Step 2: The exterior angle at C = 180° - 60° = 120°. Step 3: The bisector of the exterior angle divides it into two equal parts: 120° ÷ 2 = 60° each. Step 4: The angle between the bisector and side BC is the angle on one side of BC. Since the exterior angle is 120° and the bisector divides it equally, the angle between the bisector and BC = 60°.

Question 14

Two straight lines intersect such that one of the angles formed is 3 times the adjacent angle. If a third line is drawn parallel to one of the original lines, what is the measure of the angle that the third line makes with the other original line (in degrees)?

Accepted Answer

Step 1: When two lines intersect, adjacent angles are supplementary. Let one angle = x, then adjacent angle = 3x. Step 2: x + 3x = 180°, so 4x = 180°, giving x = 45°. The two angles are 45° and 135°. Step 3: When a line parallel to one of the original lines intersects the other original line, it makes the same angle as the original parallel line made with it (corresponding angles). The angle is 45°.

Question 15

In a triangle ABC, the exterior angle at vertex B is 110°. If the interior angle at A is 35°, find the measure of angle C (in degrees).

Accepted Answer

Step 1: The exterior angle at B equals the sum of the two non-adjacent interior angles (exterior angle theorem). So, exterior angle at B = angle A + angle C. Step 2: 110° = 35° + angle C. Step 3: angle C = 110° - 35° = 75°.

Question 16

Two parallel lines are cut by a transversal. The ratio of two co-interior angles (also called consecutive interior angles) is 4:5. What is the difference between these two angles (in degrees)?

Accepted Answer

Step 1: Co-interior angles formed by a transversal cutting parallel lines are supplementary (sum to 180°). Step 2: Let the angles be 4x and 5x. Then 4x + 5x = 180°, so 9x = 180°, giving x = 20°. Step 3: The angles are 4(20°) = 80° and 5(20°) = 100°. Step 4: Difference = 100° - 80° = 20°.

SBI Clerk Angles & Lines

Angles & Lines— Rules & Concept

Key Points to Remember

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Angles & Lines — Practice Questions

60-Second Revision — Angles & Lines