Question

20 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! .If the sizes of interior angles of a pentagon are 2xDEGREE, 3xDEGREE, 4xDEGREE, 5xDEGREE

and 6xDEGREE, find the largest interior angle of the pentagon.

Answer 1

162°

Step-by-step explanation:

Total interior angle of Pentagon:

(5 - 2) × 180

540

2x + 3x + 4x + 5x + 6x = 540

20x = 540

x = 27

Largest angle: 6x

6(27)

162

Answer 2

Answer: 162 degrees

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Step-by-step explanation:

S = 180(n-2) is the formula used to find the sum of the interior angles for any convex polygon. In this case, n = 5 sides for a pentagon

S = 180(n-2) = 180(5-2) = 180*3 = 540 degrees is the sum of the angles of the pentagon.

The angles {2x, 3x, 4x, 5x, 6x} must add to 540

2x+3x+4x+5x+6x = 540

20x = 540

x = 540/20

x = 27

Which means

2x = 2*27 = 54

3x = 3*27 = 81

4x = 4*27 = 108

5x = 5*27 = 135

6x = 6*27 = 162 is the largest interior angle