Question

PQRS is a quadrilateral with angle P is equal to angle q and angle R is equal to angle S, if Angle P is 2 times angle R find the measure of each angle

Answer 1

given
<p=<q
<r=<s
and <p=2<r
by angle sum property of quadrilateral
<p+<q+<r+<s=360
2<r+2<r+<r+<r=360
<r=360/6
=60
hence each angle measures
<p=120=<q
<r=60=<s

Answer 2

∠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 $\dfrac{360}{6}$=60 °

∴ ∠P =  ∠Q = 2 × 60 ° = 120 °  and

∠R =  ∠S = 60 °  

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