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Murljashka [212]
2 years ago
14

Given that ABCD is a parallelogram. Find the following

Mathematics
1 answer:
7nadin3 [17]2 years ago
3 0

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!

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