Question

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

Answer 1

Given a quadrilateral PQRS,

Where ∠P = 50°, ∠Q = 50° and ∠R = 60°

Now, by the angle sum property of a quadrilateral, we have

∠P + ∠Q + ∠R + ∠S = 360°

⇒ 50° + 50° + 60° + ∠S = 360°

⇒ ∠S = 360° – 160°

⇒ ∠S = 200°

Since, one interior angle of the given quadrilateral is obtuse, therefore the quadrilateral is concave.