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In this geometry problem, lines \( l_1 \) and \( l_2 \) are parallel, and they are intersected by transversals \( p \) and \( q \). The measures of angles 2 and 13 are provided as 42° and 58°, respectively, and we are asked to find the measure of angle 8.

Let's break it down step by step:

1. **Parallel Line Properties**: Since \( l_1 \) and \( l_2 \) are parallel, corresponding, alternate interior, and vertically opposite angles are equal.
  
2. **Angle 2 (42°)**: Angle 2 corresponds to angle 6 (since they are on the same side of the transversal and in corresponding positions). Therefore:
   \[
   \text{Angle 6} = 42°
   \]

3. **Angle 13 (58°)**: Angle 13 is vertically opposite angle 12, so:
   \[
   \text{Angle 12} = 58°
   \]

4. **Using Linear Pair Rule**: Angles 6 and 8 are supplementary (since they form a linear pair along line \( q \)), meaning:
   \[
   \text{Angle 6} + \text{Angle 8} = 180°
   \]
   Substituting the value of angle 6:
   \[
   42° + \text{Angle 8} = 180°
   \]
   Solving for angle 8:
   \[
   \text{Angle 8} = 180° - 42° = 138°
   \]

Thus, the measure of angle 8 is **138°**.

Do you want further clarification or more details? Here are a few related questions to expand on the topic:

1. What is the relationship between angles 1 and 5 in the figure?
2. How do alternate interior angles work in this setup?
3. How can we find the measure of angle 7 using the same principles?
4. What would change if lines \( l_1 \) and \( l_2 \) were not parallel?
5. How do you identify corresponding angles in any parallel line diagram?

**Tip:** Always check whether lines are parallel to use angle properties like alternate interior angles or corresponding angles effectively.

The measures of angles 2 and 13 are 42° and 58°. What is the measure of angle 8?

In this Grade 8 geometry problem, learn how to calculate the measure of angle 8 using parallel lines and transversals. With angles 2 and 13 given as 42° and 58°, explore key concepts like corresponding angles, linear pairs, and vertical angles. Step-by-step solution included.

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