What is the degree measure of the larger angle?

Question

A pair of complementary angles exists such that the larger of the two angles is 10 more degrees than 4 times the smaller angle.

Answer 1

The term complementary angles means, they add up to 90 degrees. So we get our first equation:

 

LargerAngle + SmallerAngle = 90 Degrees

 

The second equation we get is:

LargerAngle = 4 x SmallerAngle + 10 Degrees

 

By substitution we get:

 

(4 x SmallerAngle + 10 Degrees) + SmallerAngle = 90 Degrees

 

Simplify.

 

5 x SmallerAngle + 10 Degrees = 90 Degrees

 

Subtract 10 Degrees from both sides.

 

5 x SmallerAngle = 80 Degrees

 

Divide both sides by 5.

 

SmallerAngle = 16 Degrees

 

Substitute 16 Degrees in to the first equation

 

LargerAngle + 16 Degrees = 90 Degrees

 

Subtract 16 Degrees from both sides

 

LargerAngle = 74 Degrees