Question

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

Answer 1

By degree measure theorem, 

∠AOB = 2∠ACB 

130° = 2∠ACB 

∠ACB = 65° 

Therefore, 

∠ACB + ∠BCD = 180° 

(Linear pair) 

65o + ∠BCD = 180° 

∠BCD = 115° 

By degree measure theorem, 

Reflex ∠BOD = 2∠BCD 

Reflex ∠BOD = 2 x 115° 

= 230° 

∠BOD + Reflex ∠BOD = 360° 

(Complete angle) 

230° + x = 360° 

x = 130°