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This is a triangle where the two congruent sides indicate that it's an isosceles triangle. In such triangles, the angles opposite the congruent sides are also equal.

Given the angle of \(50^\circ\) and another angle of \(5x^\circ\), we can use the fact that the sum of all angles in a triangle must be \(180^\circ\).

Let’s solve step by step:

1. Denote the two equal angles as \(5x^\circ\).
2. We know the sum of the angles is:

\[
5x^\circ + 5x^\circ + 50^\circ = 180^\circ
\]

3. Combine like terms:

\[
10x^\circ + 50^\circ = 180^\circ
\]

4. Subtract \(50^\circ\) from both sides:

\[
10x^\circ = 130^\circ
\]

5. Divide both sides by 10:

\[
x = 13^\circ
\]

Thus, the value of \(x\) is \(13^\circ\).

Would you like further details on this, or do you have any questions? Here are some related questions:

1. What are the properties of isosceles triangles?
2. How does the triangle sum property apply to all triangles?
3. How do congruent sides relate to congruent angles in isosceles triangles?
4. Can the angles in a triangle ever exceed 180 degrees?
5. How do we solve equations involving unknown angles in geometric shapes?

**Tip:** Always remember that the sum of angles in any triangle is always 180 degrees, regardless of the triangle type!

Solve for x. Remember, congruent angles are across from congruent sides. Given a triangle with one angle labeled 50° and another angle labeled 5x°, with two congruent sides.

Learn how to solve for x in an isosceles triangle with angles of 5x° and 50°. Understand the relationship between congruent sides and angles, and apply the Triangle Angle Sum Theorem. This problem is suitable for students in Grades 7-9.

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