# If angle A is three times as large as angle B, and angles B and C sum to 90 degrees, what is the measure of each angle?

Sep 12, 2015

"A"=90º
"B"=30º
"C"=60º

#### Explanation:

We are given :
$\textcolor{red}{\left(1\right)} \text{ A"=3"B}$
and color(red)((2))" B"+"C"=90º

Assuming that all these angles are part of the same triangle

• All the angles in a triangle sum to 180º

=>color(red)((3))" A"+"B"+"C"=180º

Put $\textcolor{red}{\left(2\right)}$ in $\textcolor{red}{\left(3\right)}$
=>"A"+90º=180º=>"A"=90º

Put the value of $\text{A}$ in $\textcolor{red}{\left(1\right)}$
=>90º=3"B"=>"B"=30º

Put the value of $\text{B}$ in $\textcolor{red}{\left(2\right)}$
=>30º+"C"=90º=>"C"=60º