Question

Angle C is an inscribed angle of circle P.

Angle C measures (20x - 5)º and arc AB
measures (30x + 30)". Find the measure of
arc AB

100 degrees
50 degrees
75 degrees
150 degreea

Answer 1

150°

Explanation:

The angle at the centre subtended by arc AB is twice the inscribed angle, that is

30x + 30 = 2(20x - 5) ← distribute

30x + 30 = 40x - 10 ( subtract 40x from both sides )

- 10x + 30 = - 10 ( subtract 30 from both sides )

- 10x = - 40 ( divide both sides by - 10 )

x = 4

Hence

arc AB = (30 × 4) + 30 = 120 + 30 = 150°

Answer 2

150°

Explanation:

(30x+30)=2(20x-5)

x=4

AB=30×4+30=150