https://file.aiquickdraw.com/mathbot/file/17259700478646chhtaev.jpg

The image shows two triangles, and the problem asks to "Determine the value of \( x \)" in each triangle. Let's analyze both parts.

### a) Triangle \( \triangle PQR \)
In this triangle:
- \( \angle PQR = 54^\circ \)
- \( \angle P \) is marked with a single line, meaning it is an isosceles triangle, so \( \angle P = \angle QPR \).
- We are tasked with finding \( x \), which is the value of \( \angle PQR \).

Since the sum of angles in any triangle is always \( 180^\circ \), we can apply this rule:
\[
x + 54^\circ + x = 180^\circ
\]
\[
2x + 54^\circ = 180^\circ
\]
\[
2x = 180^\circ - 54^\circ
\]
\[
2x = 126^\circ
\]
\[
x = 63^\circ
\]

Thus, \( x = 63^\circ \) for triangle \( PQR \).

---

### b) Triangle \( \triangle ABC \)
In this triangle:
- \( \angle A = 108^\circ \)
- \( \triangle ABC \) seems to be a scalene triangle.
- We are tasked with finding \( x \), which is \( \angle BCA \).

Using the sum of angles in a triangle again:
\[
108^\circ + \angle B + x = 180^\circ
\]
Since \( \triangle ABC \) is scalene, we don't have enough information to find \( x \) directly. We need \( \angle B \) to proceed with the calculation. If more information is provided (like the value of \( \angle B \)), I can help with the full solution.

Would you like to clarify anything or ask for more details?

---

### Follow-Up Questions:
1. How do we calculate angles in an isosceles triangle?
2. What is the rule about the sum of angles in a triangle?
3. Can a triangle have an angle greater than \( 180^\circ \)?
4. What is the difference between scalene and isosceles triangles?
5. How would the solution change if \( \angle B \) in triangle \( ABC \) were provided?

### Tip:
Remember, the sum of all interior angles in any triangle is always \( 180^\circ \), no matter the type of triangle.

Determine the value of x in the given triangles. In triangle PQR, angle PQR is 54° and x is opposite to it. In triangle ABC, angle A is 108° and x is opposite to it.

Solve for the value of x in two triangles. In triangle PQR, where angle PQR is 54°, use properties of isosceles triangles to find x. In triangle ABC, with a given angle of 108°, apply the sum of angles in a triangle to solve for x.

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