Question

Given that ABCD is a parallelogram. Find the following

Answer 1

Answer:

m=8

m<A=83

m<D=97

Step-by-step explanation:

Angles that are opposite of each other in a parallelogram are equal. Knowing this, we can first conclude that angle A and angle C are equal. We can set up the following equation:

$9m+11=8m+19$

Subtract both sides by 11

$9m+11-11=8m+19-11\\9m=8m+8$

Subtract both sides by 8m

$9m-8m=8m+8-8m\\m=8$

To calculate angle A, plug the value of m into its expression.

In a parallelogram, angles that share a side are supplementary, meaning they add up to 180 degrees. Therefore, angle A and angle D are supplementary. Knowing this, we can set up the following equation:

$180=83+D$

Subtract both sides by 83

$180-83=83+D-83\\97=D$

I hope this helps!