Question

In △GHI, m∠G = (9x - 2), m∠H = (3x - 19), and m∠I = (3x + 6)". Find m∠G.

Answer 1

m∠G = 115 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees.

In triangle GHI:

`\begin{gathered} m\angle G+m\angle H+m\angle I=180\degree \\ \implies9x-2+3x-19+3x+6=180\degree \end{gathered}`

First, solve for x:

`\begin{gathered} 9x+3x+3x-2-19+6=180\degree \\ 15x-15=180\degree \\ 15x=180+15 \\ 15x=195 \\ x=(195)/(15) \\ x=13 \end{gathered}`

Therefore, the measure of angle G is:

`\begin{gathered} m\angle G=9x-2 \\ =9(13)-2 \\ =117-2 \\ m\angle G=115\degree \end{gathered}`

The measure of angle G is 115 degrees.