Question

Step 1: Draw a right triangle. Label the acute angles as angles A and B. Label the right angle as angle C. Step 2: Prove the acute angles of a right triangle are complementary. Given: Triangle ABC with angle C a right angle Prove: Angle A and angle B are complementary.

Answer 1

proved

Explanation:

In Triangle ABC angle C is 90°

Also we know that ∠A+ ∠B+∠C= 180°..........1

now since ∠C= 90°

putting ∠C= 90° in 1 we get

⇒∠A+ ∠B= 180°-90°

⇒∠A+ ∠B= 90°

Since, sum of angle A and B is 90° therefore they are complementary to each other.