Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
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Exercise 20 Page 133

The sum S of the interior angle measures of a polygon with n sides is given by the formula S=(n-2)180^(∘).

x=77

Practice makes perfect

We are given a polygon and asked to find the value of x.

polygon
To do so, let's first recall the Interior Angle Measures of a Polygon Theorem.

Interior Angle Measures of a Polygon Theorem

The sum S of the interior angle measures of a polygon with n sides is equal to the product of (n-2) and 180^(∘). S=(n-2) 180^(∘)

The given polygon has 4 sides. We can substitute this number for n in the formula to find the sum of the measures of the interior angles of the polygon.
S=(n-2) 180^(∘)
S=( 4-2) 180^(∘)
S=(2)180^(∘)
S=360^(∘)
The sum of the angle measures of the given polygon is 360^(∘). Next, we can write an equation that sets S equal to the sum of the angle measures. S= Sum of the angle measures ⇓ 360^(∘)= 60^(∘)+ 128^(∘)+ 95^(∘)+ x^(∘) Finally, we can solve this equation for x. For simplicity, we will remove the degree symbol while solving.
360=60+128+95+x
360=283+x
Solve for x
77=x
x=77