Question

A polygon is shown. U V z W 150° Y X Determine the measure of ZU? (G.10)(1 point) © A. 120° B. 60° O C. 90° O D. 240°

Answer 1

We have to find the measure of U.

The polygon has 6 sides, so it is an hexagon.

The sum of the measures of the interior angles of an hexagon is equal to:

`\begin{gathered} n=6 \\ (n-2)\cdot180\degree=(6-2)\cdot180\degree=4\cdot180\degree=720\degree \end{gathered}`

We can then write:

`m\angle U+m\angle V+m\angle W+m\angle X+m\angle Y+m\angle Z=720`

We also know that U and V have the same measure:

`m\angle U=m\angle V\longrightarrow m\angle U+m\angle V=2m\angle U`

Also X and Y have the same measure.

Then, we have:

`\begin{gathered} m\angle U+m\angle V+m\angle W+m\angle X+m\angle Y+m\angle Z=720 \\ 2m\angle U+90+150+150+90=720 \\ 2m\angle U=720-(2\cdot90+2\cdot150) \\ 2m\angle U=720-(180+300) \\ 2m\angle U=720-480 \\ 2m\angle U=240 \\ m\angle U=(240)/(2) \\ m\angle U=120 \end{gathered}`

Answer: the measure of U is 120 degrees.