Question

in a regular 20 - sided polygon, each interior angle measures select choice (with options 162°, 200°) and each exterior angle measures select choice.

Explanation:

Step1: Recall the formula for interior angle of a regular polygon

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \). For a 20 - sided polygon, \( n=20 \).
Substitute \( n = 20 \) into the formula: \( \frac{(20 - 2)\times180^{\circ}}{20}=\frac{18\times180^{\circ}}{20}=\frac{3240^{\circ}}{20} = 162^{\circ} \).

Step2: Recall the formula for exterior angle of a regular polygon

The sum of the exterior angles of any polygon is \( 360^{\circ} \). For a regular polygon with \( n \) sides, each exterior angle is \( \frac{360^{\circ}}{n} \). For \( n = 20 \), each exterior angle is \( \frac{360^{\circ}}{20}=18^{\circ} \). But in the given options for interior angle, we have \( 162^{\circ} \) which is correct for interior angle.

Answer:

For the interior angle: \( 162^{\circ} \)
For the exterior angle: \( 18^{\circ} \) (but since in the given dropdown for interior we have \( 162^{\circ} \) as an option, the interior angle is \( 162^{\circ} \))