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

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) 136°

Solution:

(c)112°​

Explanation:
Let ABCD is a parallelogram. 
  ∴ ∠​A = ∠and ∠​B = ∠D          (Opposite angles)
 Let A be the smallest angle whose measure is x.
 ∴​∠B  = (2x − 24)o
 Now, ∠​A + ∠B = 180o                (Adjacent angles are supplementary) 
   ⇒ x + 2x − 24o = 180o
   ⇒ 3x =  204o
  ⇒ x = 68o
∴​∠​B = 2 ⨯ 68o − 24o = 112o
 HenceA = C = 68o and B = D = 112o

 

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