Question

If the adjacent angles of a cyclic quadrilateral are ${40}^{\circ }$ and $100\circ$ then find all the other angles of the cyclic quadrilateral.

Answer 1

The adjacent angle are given as ${40}^{\circ }$ and ${100}^{\circ }$.

$\therefore \angle A={40}^{\circ }$ and $\angle B={100}^{\circ }$

We know that the opposite pairs of angles are supplementary to each other.

$\therefore \angle A+\angle C={180}^{\circ }$

$\Rightarrow {40}^{\circ }+\angle C={180}^{\circ }$

$\Rightarrow \angle C={180}^{\circ }-{40}^{\circ }={140}^{\circ }$

And, $\angle B+\angle D={180}^{\circ }$ [opposites angle of cyclic quadrilateral]

$\Rightarrow {100}^{\circ }+\angle D={180}^{\circ }$

$\Rightarrow \angle D={180}^{\circ }-{100}^{\circ }={80}^{\circ }$