Polygon Angle Sum Theorem

Definition: To find the sum of a polygon’s interior angles:

interior angle sum = (n – 2) 180

where n = number of sides

Example: Find the sum of the interior angles and solve for x:

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Solution: 

Use the polygon angle sum formula and solve for x.

Step 1: Identify the polygon. This polygon has 5 sides (a pentagon), so we can plug n = 5 into the formula:

Interior angle sum = (n – 2) 180
= (5 – 2) 180
= 3 * 180 = 540°
Sum = 540°

Step 2: Solve for x by writing an equation representing the sum of the angles. We know the sum is 540°, so can write:

68 + 121 + 103 + 85 + x = 540
377 + x = 540
x = 163

So we know ∠x = 163°

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