Mathematics
If one angle of a parallelogram is 90°, show that each of its angles measures 90°.
Rectilinear Figures
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Answer
Let ABCD be a parallelogram where ∠A = 90°.
Sum of adjacent angles of a parallelogram = 180°.
∠A + ∠B = 180°
90° + ∠B = 180°
∠B = 180° - 90°
∠B = 90°.
In a parallelogram, opposite angles are equal.
∠C = ∠A = 90°
∠D = ∠B = 90°.
∴ ∠A = ∠B = ∠C = ∠D = 90°
Hence, proved that all angles of parallelogram measures 90°.
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