In Fig. 16.137, O and O’ are centres of two circles intersecting at B and C. ACD is a straight line, find x .

Question

In Fig. 16.137, O and O&rsquo; are centres of two circles intersecting at B and C. ACD is a straight line, find x .

Philoid · Accepted Answer

By degree measure theorem,

∠AOB = 2 ∠ACB

130^o = 2 ∠ACB

∠ACB = 65^o

Therefore,

∠ACB + ∠BCD = 180^o (Linear pair)

65^o + ∠BCD = 180^o

∠BCD = 115^o

By degree measure theorem,

Reflex ∠BOD = 2 ∠BCD

Reflex ∠BOD = 2 * 115^o

= 230^o

∠BOD + Reflex ∠BOD = 360^o (Complete angle)

230^o + x = 360^o

x = 130^o