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Question

PQRS is a parallelogram in which QRS and PQR are in ratio 7 : 3. Find the sum of PQR  and PRQ.


  1. 147o
  2. 110o
  3. 117o
  4. 97o


Solution

The correct option is C 117o
It is given that the ratio of QRT to PQR is 7 : 3
So,
let us assume QRS=7x and PQR=3x.

Since, 
QRS and PQR are adjacent angles of the parallelogram, they are supplementary. 

So,
QRS+PQR=180o
7x+3x=180o
x=18o

By property of parallelogram, opposite angles are equal. 

So, QRS=SPQ=7x=126o and PQR=PSR=3x=54o 

The diagonal of a parallelogram divides it into two congruent triangles. 
So, the diagonal PR divides QPS and QRS into two equal halves. 

So,
PRQ=PRS=126/2=63o

Hence, PQR+PRQ=54o+63o=117o

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