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in Parallelograms by (44.3k points)

The sum of two opposite angles of a parallelogram is 130°. Find the measure of each of its angle.

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Best answer

Let ABCD be parallelogram.

Given that sum of two opposite angles of a parallelogram is 130o

Given ∠B + ∠D = 130o

∠B + ∠B = 130o [since opposite angles of a parallelogram are equal]

2∠B = 130o

∠B= 130/2 = 65o

Therefore ∠D = 65o

Also ∠B + ∠C = 180[Since ∠B and ∠C are adjacent angles]

65o+ ∠C = 180o

∠C = 180o– 65o= 115o

∠A = ∠C = 115o [since opposite angles of a parallelogram are equal]

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