Question

In △WXY, m∠W = (10x + 17), m∠X = (2x – 9), and m∠Y = (3x + 7)º. Find m∠Y.

Answer 1

m∠Y = 40º

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees. In △WXY:

`m\angle W+m\angle X+m\angle Y=180\degree`

Substitute the given values:

`(10x+17)\degree+(2x-9)\degree+(3x+7)\degree=180\degree`

First, solve for x:

`\begin{gathered} 10x+2x+3x+17-9+7=180\degree \\ 15x+15=180\degree \\ 15x=180-15 \\ 15x=165 \\ x=(165)/(15) \\ x=11 \end{gathered}`

Next, solve for the measure of angle Y:

`\begin{gathered} m\angle Y=(3x+7)º \\ =3(11)+7 \\ =33+7 \\ m\angle Y=40\degree \end{gathered}`