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In the accompanying diagram of parallelogram ABCD, angle

In the accompanying diagram of parallelogram ABCD, angle-example-1
User BachT
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In every parallelogram, the closest angles are supplementary (adjacent angles), that is, they sum up to 180º. Since B and C are adjacent angles, we have:

∠C + ∠B = 180º

2x + 12º + 5x = 180º

7x + 12º = 180º

7x = 180º - 12º

7x = 168º

x = 168º/7 ≅ 24º

After we find x, we can use its value to find angle B:

∠B = 5 * x = 5 * 24º = 120º

Now, we use the fact that in every parallelogram, two opposite angles are congruent. So, since D and B are opposite angles, we have:

∠D = ∠B

∠D ≅ 120º

User Shaneeka
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