In a parallelogram ABCD, if ∠A=(2x+5)o and ∠B=(3x−5)o, find the value of x and the measure of each angle of the parallelogram.

Question

Filo · Accepted Answer

We know that the opposite angles are equal in a parallelogram

Consider parallelogram

A BC D

So we get

∠ A = ∠ C = (2 x - 25)^{o}

∠ B = ∠ D = (3 x - 5)^{o}

We know that the sum of all the angles of a parallelogram is

360^{o}

so it can be written as

∠ A + ∠ B + ∠ C + ∠ D = 360^{o}

By subtituting the values in the above equation

(2 x + 25) + (3 x - 5) + (2 x + 25) + (3 x - 5) = 360^{o}

by addition we get

10 x + 40^{o} = 360^{o}

10 x = 320^{o}

x = 32^{o}

now substituting the value

x

∠ A = ∠ C = (2 x + 25)^{o} = (2 (32) + 25)^{o}

∠ A = ∠ C = (54 + 25)^{o}

by addition

∠ A = ∠ C = 89^{o}

∠ B = ∠ D = (3 x - 5)^{o} = (3 (32) - 5)^{o}

∠ B = ∠ D = (96 - 5)^{o}

by subtraction

∠ B = ∠ D = 91^{o}

therefore

x = 32^{o}

,

∠ A = ∠ C = 89^{o}

and

∠ B = ∠ D = 91^{o}

Question Text	In a parallelogram $A BC D$ , if $∠ A = (2 x + 5)^{o}$ and $∠ B = (3 x - 5)^{o}$ , find the value of $x$ and the measure of each angle of the parallelogram.
Answer Type	Text solution:1
Upvotes	150

In a parallelogram $A BC D$ , if $∠ A = (2 x + 5)^{o}$ and $∠ B = (3 x - 5)^{o}$ , find the value of $x$ and the measure of each angle of the parallelogram.