Chapter 1.4, Problem 51HP

To determine

To identify the sum of two acute angles.

Answer to Problem 51HP

The sum of two acute angles is sometimes obtuse.

Explanation of Solution

Given information: Two acute angles.

Evaluation:

Let’s take an example,

  $\begin{array}{l}\angle A=30°\\ \angle B=25°\end{array}$

Both the angles are acute.

And the sum is $55°$ , which is also acute.

Let’s take another example,

  $\begin{array}{l}\angle A=40°\\ \angle B=55°\end{array}$

Both the angles are acute.

And the sum is $95°$ , which is also obtuse.

Therefore, the sum of two acute angles is sometimes obtuse.