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Question
In the parallelogram ABCD, ∠A = (3x – 15)°, ∠B = (2x + 5)°. Find the values of x and ∠D.
Sum
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Solution
Given,
In the parallelogram ABCD, ∠A = (3x – 15)°, ∠B = (2x + 5)°.
The sum of the adjacent sides of a parallelogram is linear,
⇒ ∠A + ∠B = 180°
⇒ 3x – 15 + 2x + 5 = 180°
⇒ 5x = 180° + 10°
⇒ 5x = 190°
⇒ x = 38°
We know that the opposite sides of a parallelogram are equal.
⇒ ∠B = (2x + 5) = 2 × 38 + 5
⇒ ∠B = 76 + 5 = 81° = ∠D
Hence, this is required.
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