If one side of a parallelogram is 24° less than twice the smallest an

1.	If one side of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is : A. 176° B. 68° C. 112° D. 102°
Answer» Option : (C) Let the small angle be = x Then, The second angle = 2x - 24° Since, Opposite angles are equal the 4 angles will be x, 2x - 24°, x , 2x - 24° So now by angle sum property : x + 2x - 24° + x + 2x - 24° = 360° 6x - 48° = 360° 6x = 360° + 48° 6x = 408° x = \(\frac{408°}{6}\) x = 68° Thus, The smallest angle is 68° The second angle = 2 (68°) - 24° = 112°

If one side of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is : A. 176° B. 68° C. 112° D. 102°

Answer»

Option : (C)

Let the small angle be = x

Then,

The second angle = 2x - 24°

Since,

Opposite angles are equal the 4 angles will be x, 2x - 24°, x , 2x - 24°

So now by angle sum property :

x + 2x - 24° + x + 2x - 24° = 360°

6x - 48° = 360°

6x = 360° + 48°

6x = 408°

x = \(\frac{408°}{6}\)

x = 68°

Thus,

The smallest angle is 68°

The second angle = 2 (68°) - 24°

= 112°