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The sum S of the angle measures of a polygon with n sides can be found using the formula S = 180(n − 2). Write and solve an equation to find each value of x. Justify the steps in your solution. Then find the angle measures of each polygon.

The sum S of the angle measures of a polygon with n sides can be found using the formula S 180n 2 Write and solve an equation to find each value of x Justify th class=


Answer :

akposevictor

Sum of angle measures: S = 180°

Equation: (30 + x) + 9x° + 30° = 180°

Solution: x = 112

The angle measures are: 30°, 108°, and 42°.

What is the Sum of the Interior Angles of a Polygon?

The sum of the interior angles of any given polygon with n-sides can be determined using the formula, S = 180(n - 2).

The interior angles of the triangle are:

  • (30 + x)°
  • 9x°
  • 30°

The triangle has 3 side, so n = 3.

Sum of angle measures:

S = 180(n - 2) = 180(3 - 2) = 180°

Equation to be used to find x is:

(30 + x) + 9x° + 30° = 180°

Solve for x

60 + 10x = 180

10x = 180 - 60

10x = 120

10x/10 = 120/10

x = 12

Solution is: x = 12.

The measures of the other two angles would be:

(30 + x)° = (30 + 12) = 42°

9x° = 9(12) = 108°

Learn more about the sum of angle measures on:

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