Chapter 2, Problem 19CUR

To determine

To classify: the given statement as true or false for "If $\angle A=45°$ then the complement of $\angle A$ is one third of its supplement".

Answer to Problem 19CUR

The given statement is true.

Explanation of Solution

Given information:

The given statement is "If $\angle A=45°$ then the complement of $\angle A$ is one third of its supplement."

First find complement of $\angle A$

  $\angle A=45°$

As sum of two complementary angles is $90°$ ,

Complement of $\angle A=90°-45°=45°$

Now find supplement of $\angle A$

  $\angle A=45°$

As sum of two supplementary angles is $180°$ ,

Supplement of $\angle A=180°-45°=135°$

Now check whether the given statement is true or false.

Here,

Complement of $\angle A=45°=\frac{1}{3}\left(135°\right)=\frac{1}{3}$ (supplement of $\angle A$ )

So, the given statement is true.