Question

The measure of $\angle BCD$ is:

• A. ${100}^0$
• B. ${70}^0$
• C. ${80}^0$
• D. ${30}^0$

Answer 1

The correct option is C ${80}^0$

Given- $DC$ is the chord of a circle in which the quadrilateral $ABCD$ has been inscribed.

$\angle DBC={70}^o$ and $\angle BAC={30}^o$.

To find out- $\angle BCD=?$

Solution- $\angle DAC=\angle DBC={70}^o$, since the angles have been subtended by the same chord $DC$ at the cicumference.

$\therefore \angle BAD=\angle BAC+\angle DAC={70}^o+{30}^o={100}^o$

Now $\angle BCD+\angle BAD={180}^o$, since the sum of the opposite angles of a cyclic quadrilateral $={180}^o$.

$\therefore \angle BCD={180}^o-{100}^o={80}^o$