Question

In the adjoining figure AB is a diameter of the circle and $\angle$BCD = ${130}^{\circ }$. What is the value of $\angle$ABD?

• A. 30°
• B. 50°
• C. 40°
• D. none of these

Answer 1

The correct option is C

40°

$\angle$DAB + $\angle$DCB = 180 (cyclic quadrilateral)

$\angle$DAB + 130° = ${180}^{\circ }$

$\angle$DAB = ${50}^{\circ }$

$\angle$ADB = ${90}^{\circ }$ (angle subtended by a diameter)

$\angle$DBA = ${180}^{\circ }$ - $\angle$BDA - $\angle$DAB

$\angle$DBA = ${180}^{\circ }$ – ${90}^{\circ }$ – ${50}^{\circ }$

$\angle$DBA = ${40}^{\circ }$