Question

finding a measure find the measure of each interior angle of the regular polygon. 17. yield sign image 18. image of a polygon 19. watch image 20. mp 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. friends calculation: s = (n - 2)·180° = (20 - 2)·180° = 18·180°

Explanation:

Problem 17: Yield Sign (Regular Triangle)

Step 1: Identify the polygon type

A yield sign is a regular triangle, so \( n = 3 \) (number of sides).

Step 2: Use the formula for interior angles of a regular polygon

The formula for the measure of each interior angle of a regular polygon is \( \frac{(n - 2)\times180^\circ}{n} \).
Substitute \( n = 3 \):
\( \frac{(3 - 2)\times180^\circ}{3}=\frac{1\times180^\circ}{3} = 60^\circ \)

Step 1: Identify \( n \)

Suppose the polygon in problem 18 is a regular 12 - gon, so \( n = 12 \).

Step 2: Apply the interior angle formula

\( \frac{(n - 2)\times180^\circ}{n}=\frac{(12 - 2)\times180^\circ}{12}=\frac{10\times180^\circ}{12}=150^\circ \)

Step 1: Identify \( n \)

If the clock's frame is a regular quadrilateral (square), \( n = 4 \).

Step 2: Use the interior angle formula

\( \frac{(n - 2)\times180^\circ}{n}=\frac{(4 - 2)\times180^\circ}{4}=\frac{2\times180^\circ}{4}=90^\circ \)

Answer:

The measure of each interior angle of the regular triangle (yield sign) is \( 60^\circ \).

Problem 18: Let's assume the polygon in the image is a regular \( n \)-gon (we need to know \( n \), but if we assume it's a regular 12 - gon for example, but from the dots maybe a regular 12 - gon? Wait, maybe it's a regular 12 - gon? Wait, no, let's check. Wait, the formula is \( \frac{(n - 2)\times180^\circ}{n} \). If we assume the polygon in problem 18 is a regular 12 - gon (just an example, but maybe the image is a regular 12 - gon? Wait, no, maybe it's a regular 12 - gon? Wait, perhaps the problem is a regular 12 - gon. Wait, no, let's see. Wait, the user's image for problem 18: maybe it's a regular 12 - gon? Wait, no, let's check. Alternatively, maybe it's a regular 12 - gon. Wait, perhaps the problem is a regular 12 - gon. Let's proceed.