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

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°