Chapter 7.1, Problem 13PSB

To determine

The acute angles of a right triangle are complementary is to be proved.

Explanation of Solution

Given information : The following information has been given

  $\Delta ABC$ is a right triangle

  $\angle A={90}^0$

B and C are acute angles

Formula used : Sum of the angles of any triangle add up to ${180}^0$

Proof : In $\Delta ABC$ , we know that

  $\angle A={90}^0$

Now, we also know that the sum of the angles of any triangle add up to ${180}^0$

Thus, we know that

  $\angle A+\angle B+\angle C={180}^0$

Now, we substitute the value of $\angle A={90}^0$ in the equation given above. Thus, we get

  $\angle B+\angle C={90}^0$

Hence, required details are proved