In a quadrilateral PQRS, if PQ∥RS,∠S=2∠Q,PS=q and RS=p. Find the length of the side PQ.
Answer:
p+q
- Let us first draw the quadrilateral PQRS.
So, ∠S=2x
Let us join R to a point E on the side PQ such that PERS is a parallelogram. - We know that opposite sides of a parallelogram are equal.
So, ∠PSR=∠PER=2x…(i) - Also,
- The sum of angles of a triangle is
In - In
- We are given that and
As, opposite sides of a parallelogram are equal,
and
- We can see that
- Thus,