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Calculate the missing angles in the triangle below

The triangle shown is an **isosceles triangle** because it has two equal sides (indicated by the marks on sides \( a \) and \( b \)).

### Step-by-step solution:
1. One of the angles of the triangle is given as \( 50^\circ \).
2. Since the triangle is isosceles, the base angles (opposite the equal sides \( a \) and \( b \)) must be equal. Let these two angles be denoted as \( \theta \).
3. The sum of all angles in any triangle is always \( 180^\circ \).
4. Using the sum of angles property, we can write the equation:
   \[
   \theta + \theta + 50^\circ = 180^\circ
   \]
   Simplifying:
   \[
   2\theta + 50^\circ = 180^\circ
   \]
   \[
   2\theta = 180^\circ - 50^\circ
   \]
   \[
   2\theta = 130^\circ
   \]
   \[
   \theta = \frac{130^\circ}{2} = 65^\circ
   \]

Thus, the two equal angles are each \( 65^\circ \).

### Final answer:
- The two equal angles are \( 65^\circ \) each.
- The given angle is \( 50^\circ \).

Would you like further details or have any questions? 

Here are some related questions to think about:
1. What is the total sum of the angles in any polygon?
2. How does the property of equal angles in isosceles triangles affect its symmetry?
3. How would this triangle change if the given angle was larger or smaller?
4. How can you apply trigonometry to solve for the sides of an isosceles triangle?
5. How can you prove that the two other angles are equal in any isosceles triangle?

**Tip:** When solving triangle problems, always check if the triangle has any special properties like being isosceles, equilateral, or right-angled.

Learn how to calculate the missing angles in an isosceles triangle where one angle is 50°. This solution uses the isosceles triangle theorem and the angle sum property of triangles. Suitable for Grades 6-8 students.

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