Question

Solve for x. each figure is a parallelogram
left top corner T
left bottom corner S
right top corner U
right bottom corner V
Top middle 22
bottom middle -2+3x
6
8
0
12

Answer 1

It looks like you're trying to set up an equation based on the properties of a parallelogram. In a parallelogram, opposite angles are equal and the sum of angles in a quadrilateral equals 360 degrees.

To solve for \( x \), we will assume we have the following relationships based on the corners and the values you've provided:

Let's denote the angles in the parallelogram as follows:
- Angle T (top left corner)
- Angle U (top right corner)
- Angle V (bottom right corner)
- Angle S (bottom left corner)

The angles at the top corners (T and U) would have some relationship to the given angles, but without specific angle placements, I assume we're just concerned with the top and bottom angles in the middle positions:

1. Top middle angle = 22 degrees (which we can denote as angle T + angle U)
2. Bottom middle angle = -2 + 3x (which we can denote as angle S + angle V)

### Using Opposite Angles:
For the parallelogram, opposite angles are equal:
- If T + U = 22, then S + V = 22 as well.

### Using Sum of Angles:
The sum of angles in a parallelogram:
- \( (T + U) + (S + V) = 360 \):
- Since T + U = 22, then S + V = 22 as well (because opposite angles are equal).

Putting this together, it gives us:

\[
22 + (-2 + 3x) = 360
\]

Now simplifying the equation:
\[
22 - 2 + 3x = 360 \\
20 + 3x = 360
\]

To isolate \( x \), subtract \( 20 \) from both sides:
\[
3x = 360 - 20 \\
3x = 340
\]

Now, divide by \( 3 \):
\[
x = \frac{340}{3} \\
x = 113.33 \text{ (approximately)}
\]

If you have additional relationships or angles surrounding \( x \), please clarify those so I can give a more accurate answer.