Chapter 7, Problem 3CPE

To determine

To find: The supplement of an acute angle.

Answer to Problem 3CPE

A supplement of an acute angle is an obtuse angle.

Explanation of Solution

Given information: The angle is an acute angle.

Calculation:

Let the angle be $\angle A$ .

Then, its supplement is $180°-\angle A$ .

Since, the angle is acute, then,

  $\begin{array}{l}\angle A<90°\\ \Rightarrow -\angle A>-90°[\text{dividing both sides by negative]}\\ \Rightarrow \text{180}°-\angle A>180°-90°[\text{adding 180}°\text{ to both sides]}\\ \Rightarrow \text{180}°-\angle A>90°\end{array}$

So, the supplement of $\angle A$ is greater than $90°$ .

Thus, the supplement of an acute angle is an obtuse angle.