Transcript Example 4 - ClassZone

EXAMPLE 4
Find m
Apply Theorem 8.19
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
2(m
D) +204o = 360o
m
D = 78o
D for m
Combine like terms.
Solve for m
D.
F.
GUIDED PRACTICE
6.
for Example 4
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
3x + 75 + 90 + 120 = 360° quadrilateral = 360°
3x + 285 = 360° Combine like terms
3x = 75
x = 25
Subtract
Divided by 3 from each side
GUIDED PRACTICE
STEP 2
3x = 3 25
= 75
for Example 4
Substitute
Simplify
ANSWER
The value of x is 25 and the measures of the angles
that are congruent is 75