Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. ∠ 1 and ∠ 2 are supplementary angles. m ∠ 1 is 4 y + 7 , and m ∠ 2 is 9 y + 4 . Find m ∠ 2 .

Answer 1

∠ 1 and ∠ 2 are supplementary angles, supplementary angles are two angles whose sum is exactly 180, therefore:

∠ 1 + ∠ 2 = 180

Where:

∠ 1 = 4y + 7

∠ 2 = 9y + 4

Replacing the data into the equation:

4y + 7 + 9y + 4 = 180

Add like terms:

13y + 11 = 180

Subtract 11 from both sides:

13y = 180 - 11

13y = 169

Divide both sides by 13:

y = 169/13

y = 13

Replace the value of y into ∠ 1 and ∠ 2

∠ 1 = 4y + 7 = 4(13) + 7 = 52 + 7 = 59

∠ 2 = 9y + 4 = 9(13) + 4 = 117 + 4 = 121