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in Parallelograms by (30.3k points)
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Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

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Best answer

Let x be the common multiple. 

Since the sum of any two adjacent angles of a parallelogram is 180°, 

∠A + ∠B = 180° 

4x + 5x = 180° 

9x = 180° 

x = 20° 

∠A = 80° 

∠B = 100° 

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

100° + ∠C = 180° 

∠C = (180° - 100°) = 80° 

Further, ∠C + ∠D = 180° [Since, ∠C and ∠D are adjacent angles] 

80° + ∠D = 180° 

∠D = (180° - 80°) = 100° 

Therefore, ∠A = 80°, ∠B = 100°, ∠C = 80° and ∠D = 100°.

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