In the Following Figures, Find the Remaining Angles of the Parallelogram

Question

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

Sum

Solution

∠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°.

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Properties of a Parallelogram - Property: The Opposite Angles of a Parallelogram Are of Equal Measure.

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