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.

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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The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.

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