use your knowledge of interior and exterior angles to solve for both x and y in the re

Question

Accepted Answer

# Explanation:
## Step1: Find the measure of the interior angle
The figure is a regular pentagon. The formula for the measure of an interior angle of a regular polygon is $\frac{(n - 2)\times180^{\circ}}{n}$, where $n = 5$ (for a pentagon).
$$
\begin{align*}
\frac{(5 - 2)\times180^{\circ}}{5}&=\frac{3\times180^{\circ}}{5}\
& = 108^{\circ}
\end{align*}
$$
Since $4x^{\circ}$ and the interior angle of the pentagon are supplementary (they form a linear pair), we have the equation $4x+108 = 180$.
## Step2: Solve for $x$
Subtract $108$ from both sides of the equation $4x+108 = 180$.
$$
\begin{align*}
4x&=180 - 108\
4x&=72\
x&=\frac{72}{4}\
x& = 18
\end{align*}
$$
## Step3: Use the exterior - angle sum property
The sum of the exterior angles of any polygon is $360^{\circ}$. For a regular pentagon, each exterior angle is $\frac{360^{\circ}}{n}$, where $n = 5$, so each exterior angle is $72^{\circ}$. Also, we know that $12y^{\circ}$ is an exterior angle of the pentagon. Set up the equation $12y=72$.
## Step4: Solve for $y$
Divide both sides of the equation $12y = 72$ by $12$.
$$
\begin{align*}
y&=\frac{72}{12}\
y&=6
\end{align*}
$$

# Answer:
$x = 18$ and $y = 6$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the measure of the interior angle

Step2: Solve for \(x\)

Step3: Use the exterior - angle sum property

Step4: Solve for \(y\)

Answer: