Chapter 12.1, Problem 41E

To determine

To prove: that the angle $A$ and $B$ are complementary if $C$ is right angle.

Answer to Problem 41E

  $\angle A$ and $\angle B$ are complementary.

Explanation of Solution

Given:

  

The triangle $ABC$ is a right triangle.

Concept used:

Sum of the three angles of triangle is always ${180}^0$ .

If the triangle is right triangle on angle will be perpendicular or ${90}^0$ and then sum of other two angles ${90}^0$ .

Two angle that add up to ${90}^0$ are complementary.

Calculation:

According to the given diagram:

  $\angle C$ is right angle and a right triangle containone right angle.

  $\begin{array}{l}m\angle C={90}^0.\\ m\angle A+m\angle B+m\angle C={180}^0.\\ m\angle A+m\angle B={90}^0.\end{array}$

Two angle that add up to ${90}^0$ are complementary.

Hence, $\angle A$ and $\angle B$ are complementary.