Question

In fig. ABCD is a cyclic quadrilateral, O is then centre of the circle. If $\angle$ BOD = 160${}^{\circ }$, Find the measure of $\angle$BCD

• A. 50${}^{\circ }$
• B. 60${}^{\circ }$
• C. 100${}^{\circ }$
• D. 110${}^{\circ }$

Answer 1

The correct option is C 100${}^{\circ }$

$\angle BOD={160}^{\circ }$
But $\angle BAD=\frac{1}{2}\angle BOD$
$\angle BAD=\frac{1}{2}\times {160}^{\circ }={80}^{\circ }$
Since ABCD is a cyclic quadrilateral
$\therefore \angle BAD+\angle BCD={180}^{\circ }$
[$\therefore$ opposite $\angle s$ of a cyclic quadrilateral are supplementary]
$\Rightarrow {80}^{\circ }+\angle BCD={180}^{\circ }$
$\Rightarrow \angle BCD={180}^{\circ }-{80}^{\circ }={100}^{\circ }$