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 angles of parallelogram are ∠A, ∠B, ∠C, ∠D

Let smallest angle =∠A 

Let largest angle =∠B 

= ∠B = 2∠A – 24°............(i) 

∠A+∠B = 180° 

[adjacent angle of parallelogram] 

So, 

∠A+2∠A -24° = 180° 

= 3∠A = 180°+24° = 204°

= ∠A = \(\frac{204°}{3}\) = 68°

= ∠B = 2 × 68°- 24° = 112°