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In a parallelogram ABCD, ∠D= 135°, determine the measure of ∠A and ∠B.

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Let one of the adjacent angle ∠D = 135°

Therefore other adjacent angle ∠A = x°

Sum of adjacent angles = 180°

x° + 135° = 180°

x° = 180° - 135°

∠A = x° = 45°

∠A = ∠C =45° and ∠D = ∠B =135° [Measure of opposite angles of a parallelogram are equal]

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