Question

5. PORS is a quadrilateral such that P = Q. R = S. If P = 2 R. find the angles of thequadrilateral
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Answer 1

Answer:

∠P = 120 ° , ∠Q = 120 ° , ∠R = 60 ° and ∠S = 60 °

Step-by-step explanation:

Given ,

∠P = ∠Q, ∠R = ∠S and ∠P = 2∠R

To find,

the measure of each angle = ?

Solution,

By angle sum property of quadrilateral ,

∠P + ∠Q + ∠R + ∠S = 360 °

⇒ ∠P + ∠Q + ∠R + ∠S = 360 °

⇒ 2∠R + 2∠R + ∠R + ∠R = 360 °

⇒ 6∠R = 360 °

⇒ ∠R =360/6 =60 °

∴ ∠P = ∠Q = 2 × 60 ° = 120 ° and

∠R = ∠S = 60 °

Hence, ∠P = 120 ° , ∠Q = 120 ° , ∠R = 60 ° and ∠S = 60 °.