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 $$x$$?

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Uniteasy Admin · Accepted Answer

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, 
$$\dfrac{360°}{9} =  = 40° $$c
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 
$$180° − 40° = 140°$$c 
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 
$$\dfrac{140° }{2}= 70°$$c
Hence, the value of $$x$$ is 70°

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