Question

16. In the diagram below, the measure of ZW is 6 times as large as the measure of 2XWhat is the measure of angle ZWIA60°12001449D150°

Answer 1

From the diagram, angles W and X are supplementary, this means the addition of their measures is equal to 180 degrees, that is,

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

The measure of angle W is 5 times as large as the measure of angle X, then:

`m\angle W=5m\angle X`

Substituting this second equation into the first one, and solving for the measure of angle X:

`\begin{gathered} 5m\angle X+m\angle X=180\degree \\ 6m\angle X=180\degree \\ m\angle X=(180\degree)/(6) \\ m\angle X=30\degree \end{gathered}`

In consequence, the measure of angle W is:

`\begin{gathered} m\angle W=5(30\degree) \\ m\angle W=150\degree \end{gathered}`