https://file.aiquickdraw.com/mathbot/file/17274394208354e66i3uq.jpg

The triangle shown in the image is an isosceles triangle because the two sides \(DF\) and \(FE\) are marked as equal (indicated by the two equal ticks on the sides). In an isosceles triangle, the base angles are equal.

### Step-by-step solution:

1. The angles at points \(D\) and \(E\) are given as:
   - \( \angle D = 5x^\circ \)
   - \( \angle E = (3x + 14)^\circ \)

2. Since the triangle is isosceles, the angles at \(D\) and \(E\) are equal:
   \[
   5x = 3x + 14
   \]

3. Solve for \(x\):
   \[
   5x - 3x = 14
   \]
   \[
   2x = 14
   \]
   \[
   x = 7
   \]

Thus, the value of \(x\) is \(7^\circ\).

Would you like a more detailed explanation or have any other questions? Here are 5 related questions to further your understanding:

1. How would the solution change if the triangle were not isosceles?
2. How can we verify that the sum of angles in this triangle equals 180°?
3. If one angle of an isosceles triangle is 40°, what are the other angles?
4. What is the definition of an isosceles triangle, and how do we use it to solve problems?
5. How do the properties of an isosceles triangle help in geometry proofs?

**Tip:** Always check if any given triangle is isosceles or equilateral, as this simplifies angle calculations.

Solve for the value of x in an isosceles triangle where angle D is 5x° and angle E is (3x + 14)°.

This guide shows how to solve for x in an isosceles triangle, where angle D is 5x° and angle E is (3x + 14)°. It uses algebraic principles and the isosceles triangle theorem to find the value of x, suitable for students in Grades 8-10.

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