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

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 $18 0^{\circ} .$ $S = (n - 2) 18 0^{\circ}$

The given polygon has

6

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) 18 0^{\circ}

$n = 6$

S = (6 - 2) 18 0^{\circ}

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Evaluate right-hand side

Subtract term

S = (4) 18 0^{\circ}

S = 72 0^{\circ}

The sum of the angle measures of the given polygon is

72 0^{\circ} .

Next, we can write an equation that sets

S

equal to the sum of the angle measures.

S = Sum of the angle measures ⇓ 72 0^{\circ} = x^{\circ} + 12 5^{\circ} + 12 0^{\circ} + 12 5^{\circ} + 11 0^{\circ} + 13 5^{\circ}

Finally, we can solve this equation for

x .

For simplicity, we will remove the degree symbol while solving.

720 = x + 125 + 120 + 125 + 110 + 135

Add terms

720 = x + 615

▼

Solve for

x

$LHS - 615 = RHS - 615$

105 = x

Rearrange equation

x = 105

Exercise