Question

calculate the sum of the interior angles of a convex 22 - gon. 3060° 2520° 3600° 5040° none of these answers are correct. question 2 1 pts how many sides would a regular polygon have if each interior angle measures 165°? 17 24 15 22

Explanation:

Step1: Recall the formula for the sum of interior angles

The formula for the sum of interior angles of an \(n\) - sided polygon is \((n - 2)\times180^{\circ}\). Here \(n = 22\).

Step2: Substitute \(n = 22\) into the formula

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Step3: Recall the formula for the measure of an interior angle of a regular polygon

The measure of an interior angle \(\theta\) of a regular \(n\) - sided polygon is \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\). Given \(\theta = 165^{\circ}\), we set up the equation \(\frac{(n - 2)\times180^{\circ}}{n}=165^{\circ}\).

Step4: Solve the equation \(\frac{(n - 2)\times180}{n}=165\)

Multiply both sides by \(n\): \((n - 2)\times180=165n\).
Expand: \(180n-360 = 165n\).
Subtract \(165n\) from both sides: \(180n-165n-360=0\).
Simplify: \(15n=360\).
Divide both sides by \(15\): \(n = 24\).

Answer:

For the first question: \(3600^{\circ}\) (the third option).
For the second question: \(24\) (the second option).