Question

Your friend is making a pattern for quilt pieces. Her pattern is a right angle with two acute angles that complementary. The measure of one of the angles is to be 12° more than half the measure of the other angle. Find the measure of each angle of the triangle. Show your work using the format above. ​

Answer 1

Answer:

The measure of angle 1 is 52° and the measure of angle 2 is 38°

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

Let

x ----> the measure of angle 1

y ----> the measure of angle 2

we know that

$x+y=90\°$ -----> equation A

$y=\frac{x}{2}+12$ ----> equation B

Substitute equation B in equation A and solve for x

$\frac{x}{2}+12+x=90\°$

$\frac{x}{2}+x=90\°-12\°$

$\frac{3x}{2}=78\°$

$x=(2)78/3=52\°$

Find the measure of y

$y=\frac{52}{2}+12=38\°$

therefore

The measure of angle 1 is 52° and the measure of angle 2 is 38°