Question

question 9 (11.12 points) listen the last step before going live is selecting and setting up your lighting. you want the shape of the lighting design to be a polygon so that the sum of its interior angles measures 180°. based on the interior angle measures, how many sides will the shape of your chosen lighting design have? four five three six

Explanation:

Step1: Recall the formula for sum of interior angles

The formula for the sum of interior - angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon and $S$ is the sum of interior angles.

Step2: Substitute the given sum of interior angles

We are given that $S = 180^{\circ}$. Substitute $S$ into the formula: $180=(n - 2)\times180$.

Step3: Solve for $n$

Divide both sides of the equation by $180$: $1=n - 2$. Then add $2$ to both sides: $n=3$.

Answer:

C. Three