Question

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 1

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°