Question

Use the given figure to find the value of y in terms of p, q and r.

Answer 1

SR is produced to meet PQ at E.

In ΔPSE,
∠P + ∠S + ∠PES = 180°                ....(Angle sum property of a triangle)
⇒ p° + y° + ∠PES = 180°
⇒ ∠PES = 180° - p° - y°       ....(i)

In ΔRQE,
∠R + ∠Q + ∠REQ = 180°               ....(Angle sum property of a triangle)
⇒ (180° - q°) + r° + ∠REQ = 180°
⇒ ∠REQ = 180° - (180° - q°) - r°
⇒ ∠REQ = q° - r°                               ....(ii)

Now, ∠PES + ∠REQ - 180°               ....(Linear pair)
⇒ (180° - p° - y°) + (q° - r°) = 180°    ....[From (i) and (ii)]
⇒ -p° - y° + q° - r° = 0
⇒ -y° = -q° + p° + r°
⇒ y° = q° - p° - r°.