Question

placing equilateral triangles along each edge of a regular nonagon (nine-sided polygon).

What is the sum of the

measures of the pink angles?​

Answer 1

Hey Buddy

Here's the Answer

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It is a regular nonagon, so firstly we'll find the measure of each interior angles.

So sum of each interior angles of a polygon is

180° ( sides - 2 )

So, in this case side = 9

Sum all of interior angle = ( 9 - 2 ) × 180°

Sum of all interior angles = 7 × 180°

Sum of all interior angles = 1260°

Now, measure of each interior angle = 1260/9

=> 140°

Now we'll called one shaded angle and multiply it with 9 as there are nine angles and it is a regular polygon

Measure of one angle

Now in reference of above figure

Note :- interior angle of equilateral triangle is 60°

Now , by above image

x + 60° + 60° + 140° = 360°

x + 120 + 140 = 360

x + 260 = 360

x = 360 - 260

x = 100°

Measure of one angle is 100°

So sum of all angles will be = 9 × 100°

=> 900°

PEACE

:)