Question:
In figure, O and O' are centers of two circles intersecting at B and C. ACD is a straight line, find x.
Solution:
By degree measure theorem
∠AOB = 2∠ACB
⇒ 130° = 2∠ACB
⇒ ∠ACB = 130°/2 = 65°
∴ ∠ACB + ∠BCD = 180° [Liner a pair of angles]
⇒ 65° + ∠BCD = 180°
⇒ ∠BCD = 180° − 65° = 115° By degree measure theorem reflex
∠BOD = 2∠BCD
⇒ reflex ∠BOD = 2 × 115° = 230°
Now, reflex ∠BOD + ∠BO′D = 360° [Complex angle]
⇒ 230° + x = 360°
⇒ x = 360° − 230°
∴ x = 130°