Question 1

A ray stands on a straight line. If the two angles formed on either side of the ray are in the ratio 2 : 3, what is the measure of the larger angle?

Accepted Answer

Step 1: Since the ray stands on a straight line, the two angles form a linear pair and their sum = 180°. Step 2: Let the angles be 2x and 3x. Then 2x + 3x = 180° → 5x = 180° → x = 36°. Step 3: The larger angle = 3x = 3 × 36° = 108°. Therefore, the answer is 108°.

Question 2

Two parallel lines are cut by a transversal. If one of the corresponding angles is 75°, what is the measure of the other corresponding angle?

Accepted Answer

Step 1: When a transversal cuts two parallel lines, corresponding angles are equal. Step 2: If one corresponding angle is 75°, the other corresponding angle is also 75°. Therefore, the answer is 75°.

Question 3

Two lines are perpendicular to each other. If one line makes an angle of 0° with the horizontal axis, what angle does the perpendicular line make with the horizontal axis?

Accepted Answer

Step 1: If one line is horizontal (makes 0° with the horizontal axis), a perpendicular line to it must be vertical. Step 2: A vertical line makes an angle of 90° with the horizontal axis. Therefore, the perpendicular line makes 90° with the horizontal axis.

Question 4

In a triangle, one angle measures 48° and another angle measures 67°. What is the measure of the third angle?

Accepted Answer

Step 1: The sum of all angles in a triangle is 180°. Step 2: Third angle = 180° − 48° − 67° = 180° − 115° = 65°. Therefore, the third angle is 65°.

Question 5

A straight angle is divided into two angles in the ratio 2:3. What is the measure of the larger angle?

Accepted Answer

Step 1: A straight angle measures 180°. Step 2: Let the angles be 2x and 3x. Then 2x + 3x = 180°, so 5x = 180°, giving x = 36°. Step 3: The larger angle = 3x = 3 × 36° = 108°. Therefore, the answer is 108°.

Question 6

If two angles are complementary and one angle is 35°, what is the measure of the other angle?

Accepted Answer

Step 1: Two complementary angles sum to 90°. Step 2: If one angle is 35°, the other angle = 90° - 35° = 55°. Therefore, the answer is 55°.

Question 7

Three angles of a quadrilateral are 80°, 95°, and 105°. What is the measure of the fourth angle?

Accepted Answer

Step 1: The sum of all angles in a quadrilateral is 360°. Step 2: Fourth angle = 360° - 80° - 95° - 105° = 360° - 280° = 80°. Therefore, the answer is 80°.

Question 8

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the measure of the corresponding angle on the other parallel line?

Accepted Answer

Step 1: When a transversal cuts two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 72°, the other alternate interior angle is also 72°. Step 3: Corresponding angles are also equal when lines are parallel. Step 4: Therefore, the corresponding angle = 72°.

Question 9

Two lines intersect each other. 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 10

In a triangle, one angle measures 50° and another measures 70°. What is the measure of the third angle?

Accepted Answer

Step 1: The sum of all angles in a triangle is 180°. Step 2: Third angle = 180° - 50° - 70° = 60°. Therefore, the answer is 60°.

Question 11

Two lines intersect and form four angles. If one of the angles 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 12

In a triangle ABC, angle A = 50° and angle B = 60°. A line is drawn parallel to BC through point A. What is the angle between this parallel line and side AB?

Accepted Answer

Step 1: First, find angle C: angle C = 180° - 50° - 60° = 70°. Step 2: When a line through A is parallel to BC, by the alternate interior angle theorem, the angle between the parallel line and AB equals angle ABC (which is 60°). Step 3: Therefore, the angle is 60°.

Question 13

Two lines intersect such that one of the angles formed is 65°. If a third line is drawn parallel to one of the original lines, what is the measure of the corresponding angle formed with the transversal (the second original line)?

Accepted Answer

Step 1: When two lines intersect, one angle is 65°. Step 2: The adjacent angle on a straight line = 180° − 65° = 115°. Step 3: When a third line is drawn parallel to the first line, and the second line acts as a transversal, corresponding angles are equal. Step 4: The corresponding angle to the 65° angle = 65°. Therefore, the answer is 65°.

Question 14

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

Accepted Answer

Step 1: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. Step 2: Therefore, the two non-adjacent interior angles sum to 110°. Step 3: Let the angles be 3x and 2x. Step 4: 3x + 2x = 110°, so 5x = 110°, giving x = 22°. Step 5: The smaller angle = 2x = 2(22°) = 44°. Therefore, the answer is 44°.

Question 15

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the sum of the 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 is also 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 co-interior angles = 180°.

Question 16

In a triangle ABC, the angle bisector from vertex A divides the opposite side BC into segments of 6 cm and 9 cm. If the side AB = 8 cm, what is the length of side AC?

Accepted Answer

Step 1: By the Angle Bisector Theorem, the angle bisector from a vertex divides the opposite side in the ratio of the adjacent sides. Step 2: Let BD = 6 cm and DC = 9 cm (where D is on BC). Step 3: By the theorem: AB/AC = BD/DC. Step 4: 8/AC = 6/9. Step 5: 8/AC = 2/3. Step 6: AC = 8 × 3/2 = 12 cm. Therefore, the answer is 12 cm.

Question 17

In a triangle, one exterior angle measures 125°. If the two non-adjacent interior angles are in the ratio 3:2, what is the measure of the smaller non-adjacent interior angle?

Accepted Answer

Step 1: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. So the two non-adjacent interior angles sum to 125°. Step 2: Let the angles be 3x and 2x. Then 3x + 2x = 125°, so 5x = 125°, giving x = 25°. Step 3: The smaller angle = 2x = 2(25°) = 50°.

Question 18

Two lines are perpendicular to each other. A third line makes an angle of 35° with the first line. What angle does the third line make with the second line?

Accepted Answer

Step 1: The two perpendicular lines form a 90° angle between them. Step 2: If the third line makes 35° with the first line, and the two lines are perpendicular, then the third line makes an angle of 90° - 35° = 55° with the second line. Step 3: Therefore, the angle is 55°.

Question 19

Two parallel lines are cut by a transversal. One of the co-interior angles (also called consecutive interior angles) is 40° more than the other. What is the measure of the larger co-interior angle?

Accepted Answer

Step 1: Co-interior angles are supplementary, meaning they sum to 180°. Step 2: Let the smaller angle be x°. Then the larger angle is (x + 40)°. Step 3: x + (x + 40) = 180°. Step 4: 2x + 40 = 180°, so 2x = 140°, thus x = 70°. Step 5: The larger angle = 70° + 40° = 110°.

Question 20

In triangle ABC, the exterior angle at vertex A is 130°. The interior angles at B and C are in the ratio 2:3. What is the difference between the largest and smallest interior angles of the triangle?

Accepted Answer

Step 1: The exterior angle at A is 130°, so the interior angle at A = 180° - 130° = 50°. Step 2: By the exterior angle theorem, 130° = ∠B + ∠C. Step 3: Given ∠B : ∠C = 2:3, let ∠B = 2x and ∠C = 3x. Step 4: 2x + 3x = 130°, so 5x = 130°, thus x = 26°. Step 5: ∠B = 2(26°) = 52°, ∠C = 3(26°) = 78°, ∠A = 50°. Step 6: Largest angle = 78°, smallest angle = 50°. Step 7: Difference = 78° - 50° = 28°.

Question 21

In triangle ABC, the exterior angle at vertex B is 128°. If angle A is 52°, find angle C. Additionally, if a line is drawn parallel to side AC, intersecting AB at point P and BC at point Q, what is angle BPQ?

Accepted Answer

Step 1: The exterior angle at B equals 128°. By the exterior angle theorem, exterior angle at B = angle A + angle C. Therefore, 128° = 52° + angle C, which gives angle C = 76°. Step 2: The interior angle at B = 180° − 128° = 52°. Step 3: In triangle ABC, angle A + angle B + angle C = 180°, confirming 52° + 52° + 76° = 180°. Step 4: When line PQ is drawn parallel to AC, by the property of corresponding angles (or alternate interior angles), angle BPQ = angle BAC = 52°.

SSC CHSL Angles & Lines

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Angles & Lines — Practice Questions

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