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?
six
five
four
three

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

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.

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

We have \(180^{\circ}=(n - 2)\times180^{\circ}\).
Divide both sides of the equation by \(180^{\circ}\): \(\frac{180^{\circ}}{180^{\circ}}=\frac{(n - 2)\times180^{\circ}}{180^{\circ}}\).
This simplifies to \(1=n - 2\).

Step3: Solve for \(n\)

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

Answer:

Three