1. 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.

2. 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.

3. 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
= 360°
3x + 285
= 360°
Combine like terms 3x
= 75
Subtract x
= 25
Divided by 3 from each side

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