Question
ABCD is a parallelogram. Use the image to answer the question. A B D C 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) degrees
Answers
GPT-4o mini
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. This means that the sum of the interior angles at points B and D must equal 180 degrees.
Given:
- Angle B = \(3x - 7\) degrees
- Angle D = \(x + 15\) degrees
Using the property of supplementary angles, we can write the equation:
\[
(3x - 7) + (x + 15) = 180
\]
Now, simplify the equation:
\[
3x - 7 + x + 15 = 180
\]
\[
4x + 8 = 180
\]
Next, subtract 8 from both sides:
\[
4x = 172
\]
Now, divide by 4:
\[
x = 43
\]
Thus, the value of \(x\) is \(43\).
Given:
- Angle B = \(3x - 7\) degrees
- Angle D = \(x + 15\) degrees
Using the property of supplementary angles, we can write the equation:
\[
(3x - 7) + (x + 15) = 180
\]
Now, simplify the equation:
\[
3x - 7 + x + 15 = 180
\]
\[
4x + 8 = 180
\]
Next, subtract 8 from both sides:
\[
4x = 172
\]
Now, divide by 4:
\[
x = 43
\]
Thus, the value of \(x\) is \(43\).