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 the value of x?

(1 point)
Responses

30
30

10
10

20
20

60

Answer 1

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

Given:
- Angle B = \(4x - 18\)
- Angle D = \(2x + 42\)

Since angles B and D are adjacent angles, we can set up the equation:

\[
(4x - 18) + (2x + 42) = 180
\]

Now, simplify the equation:

\[
4x - 18 + 2x + 42 = 180
\]

Combine like terms:

\[
6x + 24 = 180
\]

Next, isolate \(6x\) by subtracting 24 from both sides:

\[
6x = 180 - 24
\]
\[
6x = 156
\]

Now, divide both sides by 6 to solve for \(x\):

\[
x = \frac{156}{6} = 26
\]

It appears that I made a mistake in interpreting the values of angles B and D. Let's further analyze our options. If angles B and D are in fact supposed to add up to 180 degrees, we made an error somewhere.

Additionally, we need to validate if B and D are indeed pairs of angles that can be equal or supplementary. If we analyze them based on a condition that these angles must equate to any of the options presented:

With the angles being equal, we'd have \(4x - 18 = 2x + 42\):

\[
4x - 2x = 42 + 18
\]
\[
2x = 60
\]
\[
x = 30
\]

Hence, the correct option, based on this multiplication should be \(x=30\).

The value of \(x\) is therefore 30.