Supplementary Angles Questions

Supplementary Angles Questions is a useful topic for students who want to learn geometry in a simple way. Supplementary Angles Questions help us understand two angles that add up to 180 degrees. This topic is important because it builds a strong base in maths and improves problem-solving skills. Students can practise different questions to see how supplementary angles work in real examples.

Supplementary Angles Questions with Answers

Formula for Supplementary Angles

Angle 1 + Angle 2 = 180°

If one angle = x, then the other = 180° − x

Q1: One angle is 110°. Find its supplement.

Solution: Missing angle = 180° − 110° = 70°

Q2: One angle is 45°. Find its supplementary angle.

Solution: 180° − 45° = 135°

Q3: One angle is 90°. What is its supplement?

Solution: 180° − 90° = 90°

Both angles are 90° two right angles are supplementary to each other.

Q4: Find the supplement of 67°.

Solution: 180° − 67° = 113°

Q5: Find the supplement of 178°.

Solution: 180° − 178° = 2°

Q6: Which pairs are supplementary? (a) 60° and 120° (b) 90° and 80° (c) 135° and 45°

Solution:

(a) 60° + 120° = 180°  (Supplementary)

(b) 90° + 80° = 170°    (Not supplementary)

(c) 135° + 45° = 180°  (Supplementary)

Q7: Fill in the blank: 73° and ___° are supplementary.

Solution: 180° − 73° = 107°

Q8: Fill in the blank: ___° and 154° are supplementary.

Solution: 180° − 154° = 26°

Supplementary Angles Algebra Questions

Q1: Two supplementary angles are (3x + 10)° and (2x − 5)°. Find x and both angles.

Solution: (3x + 10) + (2x − 5) = 180 5x + 5 = 180 5x = 175 x = 35

Angle 1 = 3(35) + 10 = 105 + 10 = 115° Angle 2 = 2(35) − 5 = 70 − 5 = 65°

Check: 115° + 65° = 180°

Q2: Two supplementary angles are (x + 40)° and (x − 10)°. Find x.

Solution: (x + 40) + (x − 10) = 180 2x + 30 = 180 2x = 150 x = 75

Angle 1 = 75 + 40 = 115° Angle 2 = 75 − 10 = 65°

Q3: One supplementary angle is twice the other. Find both angles.

Solution: Let the smaller angle = x. Then larger angle = 2x.

x + 2x = 180 3x = 180 x = 60

Angles are 60° and 120°.

Q4: The supplement of an angle is 30° more than the angle itself. Find the angle.

Solution: Let the angle = x. Supplement = 180 − x.

180 − x = x + 30 180 − 30 = 2x 150 = 2x x = 75°

Supplement = 180 − 75 = 105°

Check: 105 = 75 + 30

Q5: The supplement of an angle is four times the angle. Find both angles.

Solution: Let angle = x. Supplement = 4x.

x + 4x = 180 5x = 180 x = 36°

Supplement = 4 × 36 = 144°

Q6: Two supplementary angles are in ratio 2:7. Find both angles.

Solution: Let angles = 2k and 7k.

2k + 7k = 180 9k = 180 k = 20

Angles = 2 × 20 = 40° and 7 × 20 = 140°

Q7: Two supplementary angles are in ratio 5:4. Find both angles.

Solution: 5k + 4k = 180 9k = 180 k = 20

Angles = 100° and 80°

Supplementary Angles Diagram Questions

Q1: A straight line AB has a ray OC from point O on it. Angle AOC = 125°. Find angle COB.

Solution: Angles AOC and COB are on a straight line, so they form a linear pair.

Angle COB = 180° − 125° = 55°

Q2: Three angles are on a straight line 40°, x°, and 70°. Find x.

Solution: All three angles together form a straight line, so they sum to 180°.

40 + x + 70 = 180 x = 180 − 110 = 70°

Find Unknown Angles

Q3: Two angles form a linear pair. One is (7x − 4)° and the other is (5x + 16)°. Find both angles.

Solution: A linear pair is supplementary:

(7x − 4) + (5x + 16) = 180 12x + 12 = 180 12x = 168 x = 14

Angle 1 = 7(14) − 4 = 98 − 4 = 94° Angle 2 = 5(14) + 16 = 70 + 16 = 86°

Check: 94 + 86 = 180

Parallel Lines and Supplementary Angles

Q4: Two parallel lines are cut by a transversal. One co-interior angle (same-side interior angle) is 65°. Find the other co-interior angle.

Solution: Co-interior angles (also called consecutive interior angles or same-side interior angles) between parallel lines are supplementary.

Missing angle = 180° − 65° = 115°

Q5: A transversal cuts two parallel lines. One angle is 112°. Find the co-interior angle on the same side.

Solution: Co-interior angles are supplementary.

Missing angle = 180° − 112° = 68°

Supplementary Angles Word Problems

Q1: A door is opened at an angle of 70° to the wall. What angle does the door make with the remaining wall on the other side if both angles are supplementary?

Solution: Supplementary angle = 180° − 70° = 110°

The door and the remaining wall form an angle of 110°.

Q2: A straight road is split by a side lane. The side lane makes an angle of 135° with one direction of the road. What angle does it make with the other direction?

Solution: 180° − 135° = 45°

The side lane makes a 45° angle with the other direction of the road.

Q3: An architect designs a roof where two sides meet a flat ceiling. One side makes an angle of 118° with the ceiling. What angle does the other side make?

Solution: 118° + other angle = 180°

Other angle = 62°

Q4: A clock's hour hand and minute hand together form supplementary angles at 6 o'clock. If one angle is 180°, what is the supplement?

Solution: 180° − 180° = 0°

At 6 o'clock, the hands point in exactly opposite directions, forming a straight line. Both angles are 180° and 0° a degenerate supplementary pair.

Q5: Angle A and Angle B are supplementary. Angle B and Angle C are also supplementary. Prove that Angle A = Angle C.

Solution: Since A and B are supplementary: A + B = 180° → A = 180° − B. Since B and C are supplementary: B + C = 180° → C = 180° − B.

Both A and C equal (180° − B), therefore A = C. 

This shows that supplements of the same angle are always equal.

Multiple Choice Questions on Supplementary Angles

Q1: What is the supplement of 80°? (a) 10° (b) 100° (c) 180° (d) 90°

Answer: (b) 100° 180 − 80 = 100.

Q2: Two supplementary angles are equal. What is each angle? (a) 45° (b) 60° (c) 90° (d) 120°

Answer: (c) 90° x + x = 180, so x = 90.

Q3: Which pair is supplementary? (a) 40°, 50° (b) 90°, 100° (c) 75°, 105° (d) 60°, 110°

Answer: (c) 75° + 105° = 180°

Q4: The supplement of an angle is three times itself. The angle is: (a) 30° (b) 45° (c) 60° (d) 90°

Answer: (b) 45° x + 3x = 180 → 4x = 180 → x = 45.

Q5: Two supplementary angles are in ratio 3:6. The smaller angle is: (a) 30° (b) 60° (c) 90° (d) 120°

Answer: (b) 60° 3k + 6k = 180 → 9k = 180 → k = 20. Smaller = 3 × 20 = 60°.

Q6: If angle A = (2x + 5)° and its supplement = (3x − 10)°, what is x? (a) 35 (b) 37 (c) 39 (d) 41

Answer: (b) 37 (2x+5) + (3x−10) = 180 → 5x − 5 = 180 → 5x = 185 → x = 37.

Q7: Angle P and Angle Q are supplementary. Angle Q and Angle R are complementary. If Q = 40°, find P + R.

Answer: P = 180 − 40 = 140°. R = 90 − 40 = 50°. P + R = 190°.

Q8: In a linear pair, one angle is 15° more than the other. What are the angles? (a) 80°, 100° (b) 82.5°, 97.5° (c) 85°, 95° (d) 75°, 105°

Answer: (b) 82.5° and 97.5° x + (x+15) = 180 → 2x = 165 → x = 82.5.

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Read more: Complementary Angles Supplementary Angles