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:
[tex]9m+11=8m+19[/tex]
Subtract both sides by 11
[tex]9m+11-11=8m+19-11\\9m=8m+8[/tex]
Subtract both sides by 8m
[tex]9m-8m=8m+8-8m\\m=8[/tex]
To calculate angle A, plug the value of m into its expression.
[tex]<A=9m+11\\<A=9(8)+11\\<A=72+11\\<A=83[/tex]
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:
[tex]180=83+D[/tex]
Subtract both sides by 83
[tex]180-83=83+D-83\\97=D[/tex]
I hope this helps!
