Question

1. the diagram shows a convex polygon. what is the sum of the interior angle measures of this polygon? 16. the diagram shows a convex polygon. what is the sum of the interior angle measures of this polygon?

Explanation:

Question 15

Step1: Identify the number of sides

The polygon in question 15 is a nonagon (9 - sided polygon), so \( n = 9 \).

Step2: Use the formula for the sum of interior angles

The formula for the sum of the interior angles of a convex polygon is \( S=(n - 2)\times180^{\circ} \), where \( n \) is the number of sides. Substitute \( n = 9 \) into the formula:
\( S=(9 - 2)\times180^{\circ} \)
\( S = 7\times180^{\circ} \)
\( S = 1260^{\circ} \)

Step1: Identify the number of sides

The polygon in question 16 is a hexagon (6 - sided polygon), so \( n = 6 \).

Step2: Use the formula for the sum of interior angles

Using the formula \( S=(n - 2)\times180^{\circ} \), substitute \( n = 6 \):
\( S=(6 - 2)\times180^{\circ} \)
\( S = 4\times180^{\circ} \)
\( S = 720^{\circ} \)

Answer:

\( 1260 \)

Question 16