Tutorial 6.3 Examples: Using Angle Properties
Example 1:
Determine the missing angle and describe it.
52
x = 52 x 2
x = 104, central angle
x
Example 2:
Determine the missing angle and describe it.
x = 46 ÷ 2
x = 23, inscribed angle
46
x
Example 3: 37
Find the missing angle and give its
description. x
X = 24, inscribed angle subtended by
the same arc
y
Example 4:
Find all missing angles. x
x = 180 – 95
x = 85
y = 180 – 110
y = 70
95 110
Example 5: P
Find all missing angles if QRO is 42.
m n
1. S is 42 (inscribed angles subtended
by same arc) x Q
2. Q and P are 90 (angles subtended y
O
by semicircle are 90) S
3. In PQR find n using triangle angle
sum. n = 180 – 90 – 42 = 48 m = 42 42
4. In SPQ, find x using triangle angle R
sum. x = 48 y = 42
Example 6:
Find missing angle and give its description.
(use the major arc.)
x = 244 2 244
x = 122 O
x
Example 7:
Find the missing angles. 32
x = 32 x 2 = 64
m = 360 – 64 = 296
m
y = 296 2 = 148 O
x
y