1. EXAMPLE 5
Use Theorem 10.10
Find the value of each variable. a.
SOLUTION
PQRS is inscribed in a circle, so opposite angles are supplementary. a.
m P + m R = 180o
m Q + m S = 180o
75o + yo = 180o
80o + xo = 180o
y = 105
x = 100

2. EXAMPLE 5
Use Theorem 10.10
Find the value of each variable. b.
SOLUTION b.
JKLM is inscribed in a circle, so opposite angles are supplementary.
m J + m L = 180o
m K + m M = 180o
2ao + 2ao = 180o
4bo + 2bo = 180o
4a = 180
6b = 180
b = 30
a = 45

3. GUIDED PRACTICE
for Example 5
Find the value of each variable. 5.
SOLUTION
ABCD is inscribed in a circle, so opposite angles are supplementary.
m A + m C = 180o
m D+ m B = 180o
82o + xo = 180o
y°+ 68o = 180o
y = 112
x = 98

4. GUIDED PRACTICE
for Example 5
Find the value of each variable. 6.
SOLUTION
STUV is inscribed in a circle, so opposite angles are supplementary.
m S + m U = 180o
m V+ m T = 180o
c°+ (2c – 6 )o = 180o
8xo + 10xo = 180o
(3c)o = 186o
18xo = 180o
c = 62
x = 10