Question

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? six three four five

Explanation:

Step1: Recall the formula for the 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.

Step2: Substitute \(S = 180^{\circ}\) into the formula

We have \(180=(n - 2)\times180\).
Divide both sides by \(180\): \(1=n - 2\).

Step3: Solve for \(n\)

Add \(2\) to both sides of the equation: \(n=1 + 2=3\).

Answer:

Three