SOLUTION: Two of three consecutive sides of regular nonagon(nine sided) are produced to meet at point T. Calculate the size of the angle formed at T.
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Question 1201837: Two of three consecutive sides of regular nonagon(nine sided) are produced to meet at point T. Calculate the size of the angle formed at T. Found 2 solutions by math_tutor2020, greenestamps:Answer by math_tutor2020(3817) (Show Source):
A regular polygon has equal angles and equal sides.
Let's draw out a regular nonagon with 9 sides.
Highlight 3 consecutive sides.
These are adjacent neighboring sides.
I picked the 3 sides at the bottom marked in red.
Pick two sides, of those 3, that aren't neighbors. Extend them until they meet at point T.
We'll need to know the measure of each interior angle for a regular nonagon.
S = sum of interior angles of a polygon of n sides
S = 180(n-2)
S = 180(9-2)
S = 180*(9-2)
S = 1260
Then we divide that into nine equal pieces
1260/9 = 140
The measure of each interior angle of a regular nonagon is 140 degrees.
Each adjacent pair of angles marked 140 and x are supplementary.
They add to 180 degrees to form a straight line.
x+140 = 180
x = 180-140
x = 40
Focus on the triangle at the very bottom. The three interior angles add to 180.
x+x+T = 180
40+40+T = 180
80+T = 180
T = 180-80
T = 100 is the final answer.
Extending the two sides to meet at T forms a triangle with the third side of the nonagon in which two of the angles are exterior angles of the regular nonagon.
The measure of each exterior angle of a regular nonagon is 360/9 = 40 degrees.
The sum of the angles of the triangle is 180 degrees, so the measure of angle T is 180-2(40) = 100 degrees.
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