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In parallelogram ABCD, if ∠A = 2x + 15^∘, ∠B = 3x − 25^∘, then the value of x is:

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38^∘

54^∘

76^∘

84^∘

answer is A.

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Detailed Solution

ABCD is a parallelogram in which ∠A=2x+15° and ∠B=3x−25°.

We know that the sum of any two consecutive angles of a parallelogram is equal to 180°.
⇒∠A+∠B=180°

⇒2x+15°+3x−25°=180°

⇒5x=190°

⇒x= $\frac{190 °}{5}$ =38°

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