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