Question

- PQRS is a quadrilateral with <P = <Q and <R = <S. If <P = 2<R, find the measure of each angle. ​

Answer 1

answer

Step-by-step explanation:

∠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 =60 °

∴ ∠P =  ∠Q = 2 × 60 ° = 120 °  and

∠R =  ∠S = 60 °  

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