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This is an isosceles triangle because two sides are marked as equal. In an isosceles triangle, the angles opposite the equal sides are also equal.

Let's break it down:

1. One of the angles is given as \( 42^\circ \).
2. The two equal angles are labeled as \( a^\circ \) and \( b^\circ \), but since the sides are equal, \( a = b \).

### Steps to find \( a \) and \( b \):
- The sum of the angles in any triangle is always \( 180^\circ \).
- Therefore, the equation becomes:
  \[
  a + b + 42^\circ = 180^\circ
  \]
- Since \( a = b \), we can rewrite the equation as:
  \[
  2a + 42^\circ = 180^\circ
  \]
- Solving for \( a \):
  \[
  2a = 180^\circ - 42^\circ
  \]
  \[
  2a = 138^\circ
  \]
  \[
  a = \frac{138^\circ}{2} = 69^\circ
  \]

### Therefore:
- \( a = 69^\circ \)
- \( b = 69^\circ \) (since \( a = b \))

Would you like further clarification or details on this solution?

Here are 5 related questions to expand on this concept:
1. How do you determine if a triangle is isosceles based on angles and sides?
2. What is the formula for finding the sum of interior angles in a polygon?
3. How would the problem change if one of the other angles were given instead of \( 42^\circ \)?
4. Can a triangle have more than one obtuse angle? Why or why not?
5. What would happen if the given angle was \( 90^\circ \)? How would the triangle change?

**Tip:** Always check if a triangle is isosceles or equilateral when two sides or angles are marked as equal. This simplifies angle calculations!

Learn how to find the angles a and b in an isosceles triangle with a given 42° angle. This problem covers key geometric concepts such as the angle sum property and the isosceles triangle theorem. Suitable for students in Grades 6-8.

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