Q. 24.1( 22 Votes )

# Find the measure of all the angles of a parallelogram, if one angle is 24° less than the twice of the smallest angle.

Answer :

__Given:-__ one angle is 24° less than the twice of the smallest angle

__Formula used:-__ opposite angles of a parallelogram are equal

Corresponding angles sum is 180°

__Solution:-__

Let ∠ A and ∠ C be smallest because

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

2∠ A+ 24° =∠ B

∠ A+∠ B=180° [Sum of corresponding angles is 180° ]

∠ B=180°-∠ A

Then,

2∠ A+ 24° =180° -∠ A

3∠ A =180° - 24°

3∠ A=156°

∠ A==52°

∠ B=180° -∠ A

∠ B= 180° -52°

∠ B=128°

∠ B = ∠ D [opposite angles of a parallelogram are equal]

__Conclusion:-__

∴ Angles of parallelogram = 52°, 128°, 52°, 128°

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The opposite angles of a parallelogram are and Find the measure of each angle of the parallelogram.

AP- MathematicsFind the measure of all the angles of a parallelogram, if one angle is 24° less than the twice of the smallest angle.

AP- Mathematics