Question

In AWXY, m∠W = (2x – 12), m∠X = (2x + 17), and m∠Y = (9x - 7). Find m∠X.

Answer 1

45 degrees

Step-by-step explanation:

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

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

Substituting the given values:

`(2x-12)+(2x+17)+(9x-7)=180\degree`

We first solve for x.

`\begin{gathered} 2x+2x+9x=180+12-17+7 \\ 13x=182 \\ x=(182)/(13) \\ x=14 \end{gathered}`

Thus, the measure of angle X will be:

`\begin{gathered} 2x+17=2(14)+17 \\ =28+17 \\ =45\degree \end{gathered}`