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