In a || gm ABCD, if ∠A = (2x + 25)° and ∠B = (3x − 5)°,

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 =  32 − 5 = 91o
Hence, x = 32o, ∠A = C = 89o and ∠B = D = 91o 

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