In the figure, Find x°.

Theorem 1: Sum of all the angles of the triangles is 180°

In Δ COB

OD = DC

∴ ∠ COD = ∠DCO = 40°

In Δ AOB

OA = OB (Given)

∴ ∠ OAB = ∠ OBA = x°

∠ OAB + ∠ OBA + ∠ AOB = 180° (Angle Sum Property)

⇒ x° + x° + ∠ AOB = 180°

⇒ 2x° + ∠ AOB = 180°

⇒ ∠ AOB = 180° - 2x°

∠ AOB = ∠ COD (opposite angles are equal)

180 – 2x° = 40°

⇒ 180° = 40 + 2x°

⇒ 180° - 40° = 2x°

⇒ 140° = 2x°

⇒

⇒ x = 70°