Question

pqrs is a trapezium in which sp parallel to rQ , find the measures of angle p and angle r.


please tell answer ​

Answer 1

Answer:

⇒  PQRS is trapezium.

⇒   SP∥RQ           [ Given ]

We know, sum of two angles between parallel lines is supplementary

∴   ∠QRS+∠RSP=180   DEGREE

⇒  ∠QRS+90  DEGREE   =180   DEGREE

⇒  ∠QRS=180  DEGREE   −90   DEGREE  =90   DEGREE

⇒  ∠PQR+∠QRS+∠RSP+∠SPQ=360   DEGREE

⇒  100  DEGREE    +90  DEGREE +90    DEGREE +∠SPQ=360   DEGREE

⇒  280  DEGREE   +∠SPQ=360  

⇒  ∠SPQ=360 −280 =80   DEGREE

∴   Measures of ∠P and ∠R are 80  DEGREE and 90  DEGREE

 

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Answer 2

< p (angle p) = 2x

< r (angle r) = 3x

note: we can't take just "x" because just "x" won't give us the correct angle.

<p= 2x = 360°

x= 360°/2= 180°

<r= 3x = 360°

x= 360°/3= 120°

so the angles are 180° and 120°

i hope my answer helps....