Question:
In a || gm ABCD, if ∠A = (2x + 25)° and ∠B = (3x − 5)°, find the value of x and the measure of each angle of the parallelogram.
Solution:
ABCD is a parallelogram.
i.e., ∠A = ∠C and ∠B = ∠D (Opposite angles)
Also, ∠A + ∠B = 180o (Adjacent angles are supplementary)
∴ (2x + 25)° + (3x − 5)° = 180
⇒ 5x +20 = 180
⇒ 5x = 160
⇒ x = 32o
∴∠A = 2 ⨯ 32 + 25 = 89o and ∠B = 3 ⨯ 32 − 5 = 91o
Hence, x = 32o, ∠A = ∠C = 89o and ∠B = ∠D = 91o
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