Question

State the slopes of the parellel lines in the parellegram.

Quadrilateral QRST has vertices at Q (-1, 5), R (2, 8), S (4, 4), and T (1, 1). The measure of Angle Q is 108° and the measure of angle R is 108 - 2x.

Answer 1

To find the slopes of the parallel lines in the parallelogram formed by the quadrilateral QRST, we first need to determine the slopes of the sides QR, RS, ST, and TQ.

### Step 1: Calculate the slopes of each side

1. **Slope of QR:**
\[
\text{slope}_{QR} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 5}{2 - (-1)} = \frac{3}{3} = 1
\]

2. **Slope of RS:**
\[
\text{slope}_{RS} = \frac{4 - 8}{4 - 2} = \frac{-4}{2} = -2
\]

3. **Slope of ST:**
\[
\text{slope}_{ST} = \frac{1 - 4}{1 - 4} = \frac{-3}{-3} = 1
\]

4. **Slope of TQ:**
\[
\text{slope}_{TQ} = \frac{5 - 1}{-1 - 1} = \frac{4}{-2} = -2
\]

### Step 2: Identify the pairs of parallel sides

In a parallelogram, opposite sides are parallel, and thus have the same slope:

- **Sides QR and ST** have the same slope of 1.
- **Sides RS and TQ** have the same slope of -2.

### Conclusion

The slopes of the parallel lines in the parallelogram are:
- Slope of QR and ST: **1**
- Slope of RS and TQ: **-2**