Question

The exterior sides of two adjacent angles make a right angle. The first angle has a measure that is 6 more than half of the second . What are the measures of both angles ?

Answer 1

Angle 1 = 34°

Angle 2 = 56°

Explanation:

To solve, recall that a right angle equals 90°, then write an equation using the given information equalling 90°. For this problem, let the second angle equal x. So,

`x+((1)/(2)x+6)=90\\(3)/(2)x+6=90\\(3)/(2)x=84\\3x=168\\x=56`

The angle measure of the second angle is 56°. To find the angle measure of the first angle, subtract 56° from the given 90°. The first angle measure is 34°. To check:

`34=((1)/(2))(56)+6\\34=28+6\\34=34`

The derived angle measures are correct.