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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 9 Page 134

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

50

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 5 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^(∘)

n= 5

S=( 5-2) 180^(∘)

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Evaluate right-hand side

Subtract term

S=(3)180^(∘)

Multiply

S=540^(∘)

The sum of the angle measures of the given polygon is 540^(∘). Next, we can write an equation that sets S equal to the sum of the angle measures. S=Sum of the angle measures ⇓ 540^(∘)=2x^(∘)+125^(∘)+90^(∘)+125^(∘)+2x^(∘) Finally, we can solve this equation for x. For simplicity, we will remove the degree symbol while solving.

540=2x+125+90+125+2x

CommutativePropAdd

Commutative Property of Addition

540=2x+2x+125+90+125

Add terms

540=4x+340

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Solve for x

LHS-340=RHS-340

540-340=4x+340-340

Subtract term

200=4x

.LHS /4.=.RHS /4.

200/4=4x/4

Calculate quotient

50=x

Rearrange equation

x=50

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