Question

Given parallelogram ABCD, m\angle A=4x+27m ∠ A = 4 x + 27, and m\angle C=6x-23m ∠ C = 6 x − 23, find m\angle Bm ∠ B.

Answer 1

∠B = 53°

Step-by-step explanation:

In parallelogram ABCD

$\angle A=4x+27$

$\angle C=6x-23$

We know that in a parallelogram, opposite angles are equal

Therefore,

$\angle A=\angle C$

$\implies 4x+27=6x-23$

$\implies 2x=50$

$\implies x=25$

Therefore,

$\angle A=4\times 25+27=100+27=127^\circ$

Also, DA and CB sides will be parallel

AB will be transversal line to it

Therefore, sum of one side of angles will be equal to 180°

i.e. $\angle A+\angle B=180^\circ$

$\implies \angle B=180^\circ-127^\circ$

$\implies \angle B=53^\circ$

Hope this answer is helpful.

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