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To solve for \( \angle SVT \) in the given parallelogram \( STUV \), we can use the properties of parallelograms and angles.

### Step-by-step solution:

1. **Properties of a Parallelogram:**
   - Opposite angles in a parallelogram are equal.
   - Adjacent angles in a parallelogram are supplementary (i.e., they add up to \(180^\circ\)).

2. **Find \( \angle VUT \):**
   Given \( \angle STU = 135^\circ \), and since adjacent angles in a parallelogram are supplementary, we can find \( \angle VUT \) as follows:
   \[
   \angle VUT = 180^\circ - 135^\circ = 45^\circ
   \]

3. **Find \( \angle SVT \):**
   Now, look at triangle \( SVT \). Since \( \angle VSU = 48^\circ \) is given and we just calculated \( \angle VUT = 45^\circ \), we can find \( \angle SVT \) by subtracting from \( 180^\circ \) (because the angles in a triangle sum to \(180^\circ\)):
   \[
   \angle SVT = 180^\circ - (48^\circ + 45^\circ) = 180^\circ - 93^\circ = 87^\circ
   \]

Thus, \( \angle SVT = 87^\circ \).

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Do you need more details or have any questions?

Here are 5 follow-up questions related to this problem:
1. Why are opposite angles in a parallelogram always equal?
2. What other properties do parallelograms have that might help in solving geometry problems?
3. How can we verify that \( \angle VUT \) is supplementary to \( \angle STU \)?
4. What is the significance of the sum of angles in a triangle?
5. Could the solution change if the parallelogram were not "not drawn to scale"?

**Tip:** In parallelograms, always remember that adjacent angles add up to \(180^\circ\), which is a key property when dealing with angle calculations.

In the figure below, not drawn to scale, STUV is a parallelogram. ∠STU = 135°. Find ∠SVT.

Learn how to find the angle ∠SVT in a parallelogram STUV with a given angle ∠STU = 135°. This geometry problem involves the properties of parallelograms and triangles, suitable for students in Grades 8-10.

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