Question

in ABC, The sum of measures of A and B is 90°. A is 30° less than twice B use this information to find the measure of each angle

Answer 1

Given:

The sum of measures of A and B is 90°

so, we have the following equation:

$A+B=90\rightarrow(1)$

And, A is 30° less than twice B

so, we have the following equation:

$A=2B-30\rightarrow(2)$

Solving the equations (1) and (2)

Substitute with A from equation (2) into equation (1)

$\begin{gathered} 2B-30+B=90 \\ 3B=120 \\ B=\frac{120}{3}=40 \end{gathered}$

Substitute with B into equation (2) to find A:

$A=2\cdot40-30=50$

So, the answer will be:

The measure of angle A = 50

The measure of angle B = 40