Q. 34.3( 35 Votes )
Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.
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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