Question

Given that ABCD is a parallelogram. Find the following

Answer 1

m=8

m<A=83

m<D=97

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.

`<A=9m+11\\<A=9(8)+11\\<A=72+11\\<A=83`

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!