﻿ In the figure, a regular polygon with 9 sides has been divided into 9 congruent

#### Multiple Choice Question (MCQ)

In the figure, a regular polygon with 9 sides has been divided into 9 congruent isosceles triangles by line segments drawn from the center of the polygon to its vertices. What is the value of x?

1. 70\degree

2. ×

72\degree

3. ×

75\degree

4. ×

78\degree

Collected in the board: Polygon

Steven Zheng posted 4 months ago

1. The nonagon forms 9 isosceles triangles. The sum of the measures of the central angles of the 9 isosceles triangles is 360°. Since the 9 triangles are congruent, the measures of each of the central angles are the same, which is,

\dfrac{360°}{9} = = 40°

Since the sum of the measures of the interior angles of a triangle is 180°. Now we know the measure of one of the tree interior angles, the sum of the measures of the remaining two angles is

180° − 40° = 140°

Since each triangle is isosceles, the measure of each of these two angles is the same.

Therefore, the measure of each of the two angles is

\dfrac{140° }{2}= 70°

Hence, the value of x is 70°

Steven Zheng posted 4 months ago

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