Question

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

Answer 1

∠PQR + 65° = 180°    ....(Linear pair angles)
⇒ ∠PQR = 115°
PQRS is a parallelogram.
∠S = ∠Q = ∠115°   ....(Opposite angles of a parallelogram are equal)
And, ∠P + ∠S = 180°   ....(Interior angles)
⇒ ∠P + 115° = 180°
⇒ ∠P = 65°
⇒ ∠R = ∠P = 65°  ....(Opposite angles of a parallelogram are equal)
Thus, we have
∠P = 65°, ∠Q = 115°, ∠R = 65° and ∠S = 115°.