Question

ABCD is a cyclic quadrilateral. If $\angle$BCD = 100${}^{\circ }$ and $\angle$ ABD = 70${}^{\circ }$. Find $\angle$ ADB.

• A. 30°
• B. 40°
• C. 50°
• D. 60°

Answer 1

The correct option is A

30°

Given: ABCD is a cyclic quadilateral and $\angle BCD={100}^{\circ },\angle ABD={70}^{\circ }$

$\angle DAB+\angle DCB={180}^{\circ }$ [Sum of the opposite angle in the cyclic quadrilateral is ${180}^{\circ }$]

So, $\angle DAB={180}^{\circ }-{100}^{\circ }={80}^{\circ }$

Now in triangle ADB,

$\angle ADB+\angle DAB+\angle ABD={180}^{\circ }$ [Sum of angles of a triangle is ${180}^{\circ })$]
$\angle ADB+{80}^{\circ }+{70}^{\circ }={180}^{\circ }$
$\therefore \angle ADB={180}^{\circ }-{150}^{\circ }={30}^{\circ }$