Chapter 11.2, Problem 31HP

To determine

To find: Relationship between the measures of two acute angles.

Answer to Problem 31HP

Sum of two acute angles of right angled triangle is ${90}^0$

Explanation of Solution

Given information:

Triangle is Right angled

Given

Triangle is Right angled

Let $x$ and $y$ be two acute angles

We know sum of angles of a triangle is ${180}^0$

Using that

We get

  ${90}^0+x^0+y^0={180}^0$

On solving

  $\begin{array}{l}{90}^0+x^0+y^0={180}^0\\ \Rightarrow x^0+y^0={180}^0-{90}^0\\ \Rightarrow x^0+y^0={90}^0\end{array}$

Therefore,

Sum of two acute angles of right angled triangle is ${90}^0$