The figure shows a transversal that intersects two parallel lines. None of the angles are right angles. ()) Complete the sentence. $$ \angle 4 $$ and $$ \angle 8 $$ are corresponding angles. What are all the angles in the figure that are congruent to $$ \angle 2 $$ ? $$ \angle 1, \angle 7, \angle 8 $$ $$ \angle 3, \angle 5, \angle 8 $$ $$ \angle 3, \angle 6, \angle 7 $$ $$ \angle 4, \angle 6, \angle 8 $$

Question

UpStudy AI · Accepted Answer

When two parallel lines are intersected by a transversal, several pairs of angles are congruent due to their relative positions. Let's analyze the given information and determine which angles are congruent to $$ \angle 2 $$.

**Given:**
- $$ \angle 4 $$ and $$ \angle 8 $$ are corresponding angles and therefore congruent.
- The lines are parallel, and the transversal creates corresponding, alternate interior, and alternate exterior angles.

**Step-by-Step Analysis:**

1. **Corresponding Angles:**
   - $$ \angle 2 $$ corresponds to $$ \angle 6 $$. Hence, $$ \angle 2 \cong \angle 6 $$.

2. **Alternate Interior Angles:**
   - $$ \angle 2 $$ is an alternate interior angle with $$ \angle 7 $$. Therefore, $$ \angle 2 \cong \angle 7 $$.

3. **Transitive Congruence:**
   - $$ \angle 3 $$ corresponds to $$ \angle 7 $$, so $$ \angle 3 \cong \angle 7 $$.
   - Since $$ \angle 2 \cong \angle 7 $$ and $$ \angle 7 \cong \angle 3 $$, by transitivity, $$ \angle 2 \cong \angle 3 $$.

**Conclusion:**
All angles congruent to $$ \angle 2 $$ are $$ \angle 3 $$, $$ \angle 6 $$, and $$ \angle 7 $$.

**Answer:**
$$ \angle 3, \angle 6, \angle 7 $$
The angles congruent to $$ \angle 2 $$ are $$ \angle 3 $$, $$ \angle 6 $$, and $$ \angle 7 $$.

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions