In the given figure, ABCD is a cyclic quadrilateral in which BC = CD and ∠CBD = 35°. Then, ∠BAD = ?
Given: CB = CD and ∠CBD = 35°
Consider ΔBCD
Here,
CB = CD (given)
∠CBD = ∠CDB = 35° (In a triangle, angles opposite to equal sides are equal)
By angle sum property
∠BCD + ∠CBD + ∠CDB = 180°
∠BCD + 35° + 35° = 180°
∠BCD = 180° – 35° – 35° = 110°
We know that,
In a cyclic quadrilateral opposite angles are supplementary
∴ ∠BCD + ∠BAD = 180°
110° + ∠BAD = 180°
∠BAD = 180° – 110° = 70°
∴ ∠BAD = 70°