Question

Use the image of the parallelogram to answer the question.

Parallelogram upper A upper B upper C upper D is shown. Vertex upper A is on the top left. Vertex upper D is on the bottom left.

The interior angle of point B
measures(3x−7)
degrees and the interior angle of point D
measures (x+15)
degrees. What is the value of x?

(1 point)
Responses

43
43

26
26

22
22

11
11
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Answer 1

In a parallelogram, consecutive angles are supplementary, meaning they add up to 180 degrees. In this case, angles B and D are consecutive angles.

Given:
- \(\angle B = (3x - 7)\) degrees
- \(\angle D = (x + 15)\) degrees

Setting up the equation based on the supplementary property:

\[
(3x - 7) + (x + 15) = 180
\]

Now, simplify and solve for \(x\):

\[
3x - 7 + x + 15 = 180
\]
\[
4x + 8 = 180
\]
\[
4x = 180 - 8
\]
\[
4x = 172
\]
\[
x = \frac{172}{4}
\]
\[
x = 43
\]

So, the value of \(x\) is **43**.