Question

c. interior angle = 135°
\frac{n - 2(180)}{n} = 135\cdot n
n - 2(180) = 135n
180n - 360 =

Explanation:

Step1: Recall the formula for the measure of an interior angle of a regular polygon, which is $\frac{(n - 2)\times180^{\circ}}{n}$, where $n$ is the number of sides.

Given the interior angle is $135^{\circ}$, so we set up the equation $\frac{(n - 2)\times180}{n}=135$.

Step2: Multiply both sides of the equation by $n$ to eliminate the denominator.

We get $(n - 2)\times180 = 135n$.

Step3: Expand the left - hand side.

Using the distributive property, $180n-360 = 135n$.

Step4: Subtract $135n$ from both sides.

$180n - 135n-360=135n - 135n$, which simplifies to $45n-360 = 0$.

Step5: Add 360 to both sides.

$45n-360 + 360=0 + 360$, so $45n=360$.

Step6: Divide both sides by 45.

$n=\frac{360}{45}=8$.

Answer:

The number of sides of the regular polygon is 8.