Question

Two angles are complementary. The first angle measures (2x+15)°

, and the second measures (4x+9)°. Write an equation to determine the value of x. Then solve your equation and find the measures of both angles. Enter the correct answers in the boxes. Equation:

solution: x=


The first angle has a measure of
°
, and the second angle has a measure or
°

Answer 1

Part 1: (2x + 15)° + (4x + 9)° = 90°

Part 2: x = 11

Part 3: First angle = 37°

Part 4: Second angle = 53°

Explanation:

Pt. 1: When two angles are complementary, they form a right angle and their sum is 90°

Thus, the equation we can use to find x is (2x + 15)° + (4x + 9)° = 90°

Pt. 2: Now we can simply solve for x:

`(2x+15)+(4x+9)=90\\2x+15+4x+9=90\\6x+24=90\\6x=66\\x=11`

Pts 3 & 4: Now that we've solved for x, we can plug in 11 for x for both angles to find their measures.

First angle: 2(11) + 15 = 22 + 15 = 37°

Second angle: 4(11) + 9 = 44 + 9 = 53°