Question

Solve the problem15) 21 and 22 are supplementary angles. What are the measures to the nearest hundredth) of the two angles?5x - 92I

Answer 1

∠1 is 31.5°

∠2 is 148.5°.

Given:

∠1 = x

∠2 = 5x-9

The measure of ∠1 and ∠2 are supplementary angles.

First, the value of x can be calculated as,

`\begin{gathered} \angle1+\angle2=180\degree \\ 5x-9+x=180\degree \\ 6x-9=180\degree \\ 6x=180+9 \\ 6x=189 \\ x=(189)/(6) \\ x=31.5 \\ x=\angle1 \end{gathered}`

Substitute the value of x in ∠2.

`\begin{gathered} \angle2=5x-9 \\ =5(31.5)-9 \\ =157.5-9 \\ =148.5 \end{gathered}`

Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.