Question

In the given figure, ABCD is a cyclic quadrilateral in which BC = CD and $\angle CBD={35}^{\circ }$. Find $\angle BAD$.

• A. 80°
• B. 65°
• C. 70°
• D. 60°

Answer 1

The correct option is C 70°

BC = CD (given)
⇒ $\angle BDC$ = $\angle CBD$ = 35°

In Δ BCD, we have:
$\angle BCD$ + $\angle BDC$ + $\angle CBD$ = 180° (Angle sum property of a triangle)
⇒ $\angle BCD$ + 35° + 35° = 180°
⇒ $\angle BCD$ = (180° - 70°) = 110°

In cyclic quadrilateral ABCD, we have:
$\angle BAD$ + $\angle BCD$ = 180°
⇒ $\angle BAD$ + 110° = 180°
⇒ $\angle BAD$ = 180° - 110° = 70°

$\therefore$ Option b is the correct answer.