please help
Figure ABCD is a parallelogram.

What are the measures of angles B and D?

∠B = 55°; ∠D = 55°
∠B = 55°; ∠D = 125°
∠B = 97°; ∠D = 97°
∠B = 83°; ∠D = 97°

please help Figure ABCD is a parallelogram What are the measures of angles B and D B 55 D 55 B 55 D 125 B 97 D 97 B 83 D 97 class=

Respuesta :

One basic property of a parallelogram is that opposite angles have the same value. Hence angle B = angle D. (2n+15°) = (3n-5°). Then have one side for the unknown. The equation will be 3n=2n+15°+5°. To get the n, simplify the equation: 3n-2n = 20° or n = 20°. Afterwards substitute the value of n to the angles. Angle B = (2(20)+15), Angle D = (3(20)-5). Lastly, simplify the equations. Angle B = (40+15°) = 55° and Angle D = (60-5°)=55°. Therefore the value of angles B & D are both 55°.

The value of both the angles is 55 degrees. Thus, option (A) is correct.

ABCD is a parallelogram in which the measures of angle D and angle B are given.

The measure of angle D is (3n-5).

The measure of angle B is (2n+15).

Now, we know that the opposite angles of a parallelogram are always congruent to each other.

Therefore,

[tex]\angle B= \angle D\\2n+15=3n-5\\n=20[/tex]

Thus, the value of n is 10.

Now,

[tex]\begin{aligned}\angle B&=2 \times 20+15\\&=55 \end{aligned}[/tex]

[tex]\begin{aligned}\angle D&=3 \times 20-5\\&=55 \end{aligned}[/tex]

Hence, the value of both the angles is 55 degrees. Thus, option (A) is correct.

To know more about the parallelograms, please refer to the link:

https://brainly.com/question/17324177

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