1. 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 =
360
Combine like terms.
x = 72
Subtract 288 from each side.
The value of x is 72.
ANSWER

2. 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) = x
Polygon Interior Angles Theorem = 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

3. 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