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witch one is right

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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

22
22

26
26

11
11

43

1 answer

In a parallelogram, opposite angles are equal and adjacent angles are supplementary (i.e., they add up to 180 degrees).

In this case, angle B and angle D are adjacent angles. Therefore, we can set up the equation:

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

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

  1. Combine like terms: \[ 3x - 7 + x + 15 = 180 \] \[ 4x + 8 = 180 \]

  2. Subtract 8 from both sides: \[ 4x = 172 \]

  3. Divide by 4: \[ x = 43 \]

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