Question

1. smp.3 you be the teacher your friend finds the measure of each interior angle of a regular 20 - gon. is your friend correct? explain your reasoning.
2. connecting to real life the border of a susan b. anthony dollar is a regular polygon. what is the measure of each interior angle of the border? round your answer to the nearest degree. (see example 3.)

Explanation:

Step1: Calculate 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. For a \(20 -\)gon, \(n = 20\).

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Step2: Calculate the measure of each interior angle

Since it is a regular \(20 -\)gon (all interior angles are equal), the measure of each interior angle \(A=\frac{S}{n}\). Substitute \(S = 3240^{\circ}\) and \(n = 20\) into the formula.

$$ A=\frac{3240^{\circ}}{20}=162^{\circ} $$

Your friend made a mistake in the last step. They divided by \(18\) instead of \(20\).

Answer:

Your friend is incorrect. The measure of each interior angle of a regular \(20 -\)gon is \(162^{\circ}\).