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Question
In the given figure, `square`PQRS and `square`ABCR are two parallelograms. If ∠P = 110° then find the measures of all angles of `square`ABCR.
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Solution
`square`PQRS is a parallelogram. ...[Given]
∴ ∠R = ∠P ...[Opposite angles of a parallelogram]
∴ ∠R = 110° ...(i)
`square`ABCR is a parallelogram. ...[Given]
∴ ∠A + ∠R = 180° ...[Adjacent angles of a parallelogram are supplementary]
∴ ∠A + 110° = 180° ...[From (i)]
∴ ∠A = 180° - 110°
∴ ∠A = 70°
∴ ∠C = ∠A = 70°
∴ ∠B = ∠R = 110° ...[Opposite angles of a parallelogram]
∴ ∠A = 70°, ∠B = 110°,
∴ ∠C = 70°, ∠R = 110°
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