EXAMPLE 4 Apply Theorem 8.19 Find m D in the kite shown at the right.

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Presentation transcript:

EXAMPLE 4 Apply Theorem 8.19 Find m D in the kite shown at the right. SOLUTION By Theorem 8.19, DEFG has exactly one pair of congruent opposite angles. Because E G, D and F must be congruent.So, m D = m F.Write and solve an equation to find m D.

EXAMPLE 4 Apply Theorem 8.19 m D + m F +124o + 80o = 360o Corollary to Theorem 8.1 m D + m D +124o + 80o = 360o Substitute m D for m F. 2(m D) +204o = 360o Combine like terms. m D = 78o Solve for m D.

GUIDED PRACTICE for Example 4 6. In a kite, the measures of the angles are 3xo, 75o, 90o, and 120o. Find the value of x. What are the measures of the angles that are congruent? SOLUTION STEP 1 Sum of the angles in a quadrilateral = 360° 3x + 75 + 90 + 120 = 360° 3x + 285 = 360° Combine like terms 3x = 75 Subtract x = 25 Divided by 3 from each side

for Example 4 GUIDED PRACTICE STEP 2 3x = 3 25 = 75 ANSWER = 3 25 Substitute = 75 Simplify The value of x is 25 and the measures of the angles that are congruent is 75 ANSWER