Question

PQRS is a quadrilateral such that angle p = angle Q ,angle R = angle S . if angle p = 2 angle R find the angles of the quadrilateral ​

Answer 1

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∠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 = ?

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 °.

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Answer 2

To Find :

• Measure of all angles of quadrilateral.

Solution :

• ∠p = ∠Q
• ∠R = ∠S
• ∠P = 2∠R

We know that,

• Sum of all angles of quadrilateral is 360°

So,

›› ∠P + ∠Q + ∠R + ∠S = 360 °

As it is given that ∠p = ∠Q ,∠R = ∠S and ∠P = 2∠R

Then,

›› 2∠R + 2∠R + ∠R + ∠R = 360

›› 4∠R + 2∠R = 360

›› 6∠R = 360

›› ∠R =360/6

• ∠R = 60°

Measure of all angles :

∠p = 2∠R

∠p = 2 × 60

• ∠p = 120°

∠p = ∠Q

• ∠Q = 120°

∠R = ∠S

• ∠S = 60°

Hence

• Measure of all angles of quadrilateral are 60° , 60° , 120° and 120°

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