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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