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EXAMPLE 3

ALGEBRA. Find the value of x in the diagram shown. x° + 108° + 121° + 59° =. 360°. 360. x + 288 =. x =. 72. The value of x is 72. ANSWER. EXAMPLE 3. Find an unknown interior angle measure. SOLUTION.

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EXAMPLE 3

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  1. ALGEBRA Find the value of xin the diagram shown. x° + 108° + 121° + 59° = 360° 360 x + 288 = x = 72 The value of xis 72. ANSWER EXAMPLE 3 Find an unknown interior angle measure SOLUTION The polygon is a quadrilateral. Use the Corollary to the Polygon Interior Angles Theorem to write an equation involving x. Then solve the equation. Corollary to Theorem 8.1 Combine like terms. Subtract 288 from each side.

  2. 3. The values of T and S = 103° each. Use the diagram at the right. Find mSand mT. (5 – 2) 180 = x 3 180 = x 540 = x T + S + 93° + 156° + 85° = 540 2 T = 206 T = 103 ANSWER for Example 3 GUIDED PRACTICE SOLUTION STEP 1 Polygon Interior Angles Theorem Subtract. Multiply. STEP 2 Corollary to Theorem 8.1 Combine like terms. Divide 2 from each side

  3. 4. The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle. x° + 89° + 110° + 46° = 360° x + 245° = 360° x = 115° for Example 3 GUIDED PRACTICE SOLUTION Corollary to Theorem 8.1 Combine like terms. Subtract 245 from each side

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