Question

2 angles are complementary. the larger angle is 30 degrees more than 4 times the smaller angle. find the measure of each angle

Answer 1

Answer:

The smaller angle is 12° and the larger angle is 78°.

Step-by-step explanation:

Complementary angles

Complementary angles are angles that add up to 90°.

We can let $x$ = the smaller angle.

Thus, given that the larger angle is 30 more than 4 times the smaller angle, larger angle must be: $4x+30$.

We can add these two expressions and set them equal to 90.

$x+4x+30=90$

Combine like terms.

$5x+30=90$

$5x=60$

$x=12$

The smaller angle is 12°.

Substitute $x$ to solve for the larger angle.

$4(12)+30$

$48+30$

$78$°

The larger angle is 78°.