Question

1. choose the correct answer.

a polygon that is equiangular but not equilateral, or equilateral but not equiangular, or neither equiangular nor equilateral is a(n)____
vertex of a polygon
convex polygon
irregular polygon
regular polygon

1. choose the correct answer.

the polygon interior angle sum theorem states that the sum of the measures of the interior angles of a convex polygon with n sides is____
$(n - 2)360^{circ}$
$(n + 2)180^{circ}$
$(n - 2)180^{circ}$
$(n + 2)360^{circ}$

Explanation:

9.

Step1: Recall definitions

• A vertex of a polygon is a point where two sides meet.
• A convex polygon has all interior angles less than \(180^{\circ}\).
• A regular polygon is both equiangular (all angles equal) and equilateral (all sides equal).
• An irregular polygon is not regular, i.e., it is equiangular but not equilateral, or equilateral but not equiangular, or neither.

10.

Step1: Recall the Polygon Interior Angle Sum Theorem

The formula for the sum of the interior angles of a convex polygon with \(n\) sides is \((n - 2)\times180^{\circ}\). For example, a triangle (\(n = 3\)) has \((3-2)\times180^{\circ}=180^{\circ}\), a quadrilateral (\(n = 4\)) has \((4 - 2)\times180^{\circ}=360^{\circ}\).

Answer:

1. irregular polygon
2. \((n - 2)180^{\circ}\)