Find an unknown interior angle measure

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Presentation transcript:

Find an unknown interior angle measure EXAMPLE 3 Find an unknown interior angle measure ALGEBRA Find the value of x in the diagram shown. 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. x° + 108° + 121° + 59° = 360° Corollary to Theorem 8.1 x + 288 = 360 Combine like terms. x = 72 Subtract 288 from each side. The value of x is 72. ANSWER

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

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