Question

In the following figures, find the remaining angles of the  parallelogram

Answer 1

PQRS is a parallelogram.
∠Q = 60°
⇒ ∠S = 60°    ....(Opposite angles of a parallelogram are equal)
In ΔPQR,
∠RPQ + ∠PQR + ∠PRQ = 180°  ....(Angle sum property of a triangle)
⇒ 50° + 60°+ ∠PRQ = 180°
⇒ 110° + ∠PRQ = 180°
⇒ ∠PRQ = 70°
And, ∠SPR = ∠PRQ = 70°  ....(Alternate angles)
⇒ ∠SPQ
= ∠SPR + ∠RPQ
= 70° + 50°
= 120°
⇒ ∠SRQ = 120°   ....(Opposite angles of a parallelogram are equal)
Thus, we have
∠P = 120°, ∠S = 60° and ∠R =120°.