Answer:
21) 130
22) 146
23) 113
24) 150
Explanation:
21)
m<BAC = 50
m<BAO = m<CAO = (1/2)m<BAC = (1/2)(50) = 25
A radius intersects a tangent at a right angle, so m<B = 90.
m<BAO + m<B + m<AOB = 180
25 + 90 + m<AOB = 180
m<AOB = 65
m<BOC = 2 × m<AOB = 2 × 65 = 130
22)
m<BAC = 34
m<BAO = m<CAO = (1/2)m<BAC = (1/2)(34) = 17
A radius intersects a tangent at a right angle, so m<B = 90.
m<BAO + m<B + m<AOB = 180
17 + 90 + m<AOB = 180
m<AOB = 73
m<BOC = 2 × m<AOB = 2 × 73 = 146
23)
m<AOB = (1/2)m<BOC = (1/2) × 67 = 33.5
m<BAO + m<B + m<AOB = 180
m<BAO + 90 + 33.5 = 180
m<BAO = 56.5
m<BAC = 2 × m<BAO = 2 × 56.5 = 113
24)
m<AOB = (1/2)m<BOC = (1/2) × 30 = 15
m<BAO + m<B + m<AOB = 180
m<BAO + 90 + 15 = 180
m<BAO = 75
m<BAC = 2 × m<BAO = 2 × 75 = 150