Question

In a quadrilateral $ABCD$, $\angle A={60}^o,\angle B={105}^o$ and $\angle D={50}^o$. Find $\angle C$.

Answer 1

In a quadrilateral $ABCD,$

$\angle A={60}^o,\angle B={105}^o$ and $\angle D={50}^o$.

We know, by angle sum property, in a quadrilateral sum of four angles is ${360}^o.$

$\therefore$ $\angle A+\angle B+\angle C+\angle D={360}^o$

$\Rightarrow$ ${60}^o+{105}^o+\angle C+{50}^o={360}^o$

$\Rightarrow$ ${215}^o+\angle C={360}^o$

$\Rightarrow$ $\angle C={145}^o$.

Hence, ${145}^o$ is the answer.