Abcd is a parallelogram.If A = 4x-13 and D is 5x -22 find the value of x
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Abcd is a parallelogram.If A = 4x-13 and D is 5x -22 find the value of x
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Answer:
Let ∠B = x.
Then, ∠A = 3x.
We know that opposite sides of a parallelogram are equal.
⇒ ∠A = ∠C = 3x
⇒ ∠B = ∠D = x.
We know that Sum of the parallelogram angles is equal to 360°.
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ 3x + x + 3x + x = 360°
⇒ 8x = 360°
⇒ x = 45°.
Then,
⇒ 3x = 3(45) = 135.
Hence, the angles are : 135°,45°,135°,45°.
Now,
Given that AB = 5x - 7 and CD = 3x + 1
We know that opposite sides of a parallelogram are equal.
⇒ AB = CD
⇒ 5x - 7 = 3x + 1
⇒ 2x = 8
⇒ x = 4.
Substitute x in CD, we get
⇒ 3x + 1
⇒ 3(4) + 1
⇒ 13.
Therefore, the length of CD = 13.
Hope it helps!
Step-by-step explanation: