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°

Answer 1

(c)112°​

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