Question

Question 165
In a quadrilateral PQRS, $\angle P={50}^{\circ },\angle Q={50}^{\circ },\angle R={60}^{\circ }$. Find $\angle S$. Is this quadrilateral convex or concave?

Answer 1

Given a quadrilateral PQRS, where
$\angle P={50}^{\circ },\angle Q={50}^{\circ }$ and $\angle R={60}^{\circ }$
Now, by the angle sum property of a quadrilateral, we have
$\angle P+\angle Q+\angle R+\angle S={360}^{\circ }\Rightarrow {50}^{\circ }+{50}^{\circ }+{60}^{\circ }+\angle S={360}^{\circ }\Rightarrow \angle S={360}^{\circ }-{160}^{\circ }\Rightarrow \angle S={200}^{\circ }$
One interior angle of the given quadrilateral is greater than ${180}^{\circ }$, therefore the quadrilateral is concave.