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Given that ABCD is a parallelogram. Find the following

Given that ABCD is a parallelogram. Find the following-example-1
User Troutwine
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1 Answer

8 votes

Answer:

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!

User Montrealist
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