# In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?

**Solution:**

Given, PQRS is a __quadrilateral__.

∠P = 50°, ∠Q = 50° and ∠R = 60°.

We have to find ∠S.

Let ∠S = x.

We know that the sum of all angles of a quadrilateral is 360 degrees.

So, ∠P + ∠Q + ∠R + ∠S = 360°

50° + 50° + 60° + x = 360°

160° + x = 360°

x = 360° - 160°

x = 200°

Therefore, ∠S = 200°

We have to find whether the quadrilateral is convex or concave.

Concave quadrilaterals are four sided polygons that have one interior angle greater than

180°.

Since the interior angle S is greater than 180°, the PQRS is a concave quadrilateral.

Therefore, PQRS is a concave quadrilateral.

**✦ Try This: **In a quadrilateral ABCD, ∠A = 70°, ∠B = 80°, ∠C = 160°. Find ∠D. Is this quadrilateral convex or concave?

**☛ Also Check: **NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 165**

## In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?

**Summary:**

In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. The value of ∠S = 200°. This quadrilateral is concave.

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