Question
In the parallelogram ABCD, the interior angle of point B measures (4x-18) degrees and the interior angle of point D measures (2x+42) degrees. What is value of x? choose the correct answer
a. 60
b. 20
c. 10
d. 30
a. 60
b. 20
c. 10
d. 30
Answers
GPT-4o mini
In a parallelogram, the sum of adjacent angles is 180 degrees. Therefore, we can set up the equation for angles B and D as follows:
\[
(4x - 18) + (2x + 42) = 180
\]
Now, simplify this equation:
\[
4x - 18 + 2x + 42 = 180
\]
Combine like terms:
\[
(4x + 2x) + (-18 + 42) = 180
\]
\[
6x + 24 = 180
\]
Next, subtract 24 from both sides:
\[
6x = 180 - 24
\]
\[
6x = 156
\]
Now, divide by 6:
\[
x = \frac{156}{6} = 26
\]
Since none of the options (60, 20, 10, 30) match 26, it appears there might be some discrepancy with the choices provided. Please double-check the provided answers or the problem. However, based on the calculations, the value of \( x \) is \( 26 \).
\[
(4x - 18) + (2x + 42) = 180
\]
Now, simplify this equation:
\[
4x - 18 + 2x + 42 = 180
\]
Combine like terms:
\[
(4x + 2x) + (-18 + 42) = 180
\]
\[
6x + 24 = 180
\]
Next, subtract 24 from both sides:
\[
6x = 180 - 24
\]
\[
6x = 156
\]
Now, divide by 6:
\[
x = \frac{156}{6} = 26
\]
Since none of the options (60, 20, 10, 30) match 26, it appears there might be some discrepancy with the choices provided. Please double-check the provided answers or the problem. However, based on the calculations, the value of \( x \) is \( 26 \).