Question

ABCD is a cyclic quadrilateral, in which $\angle$DBC =80${}^{\circ }$ and $\angle$BAC = 40${}^{\circ }$ . Find $\angle$BCD.

• A. 30°
• B. 40°
• C. 50°
• D. 60°

Answer 1

The correct option is D

60°

Given, In cyclic quadilateral ABCD,

$\angle$DBC= 80${}^{\circ }$ ,$\angle$BAC =40${}^{\circ }$

To find $\angle$BCD,

$\angle$DBC= $\angle$DAC (Angles in same segment) $\angle$DBC =80${}^{\circ }$

Now, $\angle$DAB = $\angle$DAC+ $\angle$CAB = 80${}^{\circ }$+40${}^{\circ }$=120${}^{\circ }$

Then, $\angle$DAB +$\angle$BCD =180${}^{\circ }$

120^\circ\)+$\angle$BCD= 180${}^{\circ }$

$\angle$BCD= 180${}^{\circ }$- 120${}^{\circ }$ =60${}^{\circ }$