Question

If one angle of a parallelogram is 24° less than twice the smallest angle then the largest angle of the parallelogram is 

A. 68° 

B. 102° 

C. 112° 

D. 176°

Answer 1

Let ∠A = x°, 

∠B = (2x – 24)° 

∠C = x° (Opposite angles are equal.) 

∠D = (2x – 24)° (Opposite angles are equal.) 

Since the sum of angles of a parallelogram is 360°, 

∠A + ∠B + ∠C + ∠D = 360° 

x° + (2x – 24)° + x° + (2x – 24)° = 360° 

6x° – 48 = 360° 

6x° = 408° 

x° = 68° 

∠A = 68° 

∠B = (2x – 24)° = 112° 

Therefore, largest angle of the parallelogram is 112°.