Question

Find m/CDE.

A
2x-13
B(2x+9
C
2x+11
3x-8
2x-3) F
2x-7
E
3x-1
D
m/CDE = [?] degrees

Answer 1

∠CDE = 170°

Explanation:

You want the measure of angle D in the heptagon shown.

Angles

The sum of angles in a heptagon is 180°(7 -2) = 900°. This means ...

(2x -13) +(2x +9) +(2x +11) +(3x -1) +(2x -7) +(2x -3) +(3x -8) = 900

16x = 912 . . . . . . . add 12

x = 912/16 = 57

Angle D = 3x -1 = 3(57) -1 = 170

The measure of angle CDE is 170°.

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Additional comment

The sum of interior angles of an n-sided polygon is (n -2)·180°.

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