Question

# PQRS is a parallelogram in which ∠QRS and ∠PQR are in ratio 7 : 3. Find the sum of ∠PQR  and ∠PRQ. 147o110o117o97o

Solution

## The correct option is C 117oIt 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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