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.
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°
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
2∠ A+ 24° =180° -∠ A
3∠ A =180° - 24°
∠ B=180° -∠ A
∠ B= 180° -52°
∠ B = ∠ D [opposite angles of a parallelogram are equal]
∴ Angles of parallelogram = 52°, 128°, 52°, 128°
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