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 = ∠C 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
Hence, ∠A = ∠C = 68o and ∠B = ∠D = 112o