Question

1. Sketch a hexagon that is equiangular but not equilateral.
2. What is its interior angle sum?
3. What is its exterior angle sum?

Short answer

a. The sketch of a hexagon that is equiangular but not equilateral is:

b. The interior angle sum is $720°$.

c. The exterior angle sum is $360°$.

Step-by-step solution

Part a. Step 1. Definition of equiangular.

Equiangular means the angles have same measures.

Part a. Step 2. Definition of equilateral.

Equilateral means the sides have same measures.

Part a. Step 3. Sketch the hexagon that is equiangular but not equilateral.

The sketch of the hexagon that is equiangular but not equilateral is:

Part b. Step 1. Write the theorem for the sum of interior angles of polygon.

The theorem for the sum of interior angles of polygon is that the sum of the measures of the interior angles of the polygon with sides is $\left(n-2\right)\mathbf{180}$.

Part b. Step 2. Find the value of n.

The number of sides in hexagon is 6.

Therefore, the value of$n$is 6.

Part b. Step 3. Find the sum of interior angles of hexagon.

The sum of the interior angles of the hexagon is given by:

$$\begin{gathered} \left(6-2\right)180=4\times 180 \\ =720 \end{gathered}$$

Therefore, the sum of the interior angles of the hexagon is $720°$.

Part c. Step 1. Write the theorem for the sum of exterior angles of polygon.

The theorem for the sum of exterior angles of polygon is that the sum of the measures of the exterior angles of the polygon is $\mathbf{360}\mathbf{°}$.

Part c. Step 2. Find the value of n.

The number of sides in hexagon is 6.

Therefore, the value of$n$is 6.

Part c. Step 3. Find the sum of exterior angles of hexagon.

Therefore, the sum of the exterior angles of the hexagon is $360°$.