Question

show all work for full credit. part a – fill in the blank (5 questions) 1. the sum of the interior angles of an n - sided polygon is given by the formula _. 2. a hexagon has interior angles. 3. in a regular polygon, the measure of one exterior angle is found by dividing by the number of sides. 4. the sum of the exterior angles of any polygon is always . 5. a polygon with an interior angle sum of 1980° has __ sides.

Explanation:

Step1: Recall interior - angle formula

The sum of the interior angles of an n - sided polygon is given by the formula $(n - 2)\times180^{\circ}$.

Step2: Identify number of interior angles in a hexagon

A hexagon has 6 sides and 6 interior angles.

Step3: Recall exterior - angle formula

In a regular polygon, the measure of one exterior angle is found by dividing $360^{\circ}$ by the number of sides.

Step4: Recall sum of exterior angles

The sum of the exterior angles of any polygon is always $360^{\circ}$.

Step5: Solve for number of sides given interior - angle sum

Let $(n - 2)\times180^{\circ}=1980^{\circ}$. First, divide both sides by $180^{\circ}$: $n - 2=\frac{1980^{\circ}}{180^{\circ}} = 11$. Then add 2 to both sides: $n=11 + 2=13$.

Answer:

1. $(n - 2)\times180^{\circ}$
2. 6
3. $360^{\circ}$
4. $360^{\circ}$
5. 13