Question

Parallel lines x and w are cut by transversals z and y and form 4 angles at each intersection. Where line x intersects with line z, labeled clockwise, from the uppercase left, the angles are: 1, 4, 3, 2. Where line w intersects with line z, the angles are: 5, 75 degrees, 7, 6. Where line x intersects with line x, the angles are: 13, 16, 15, 14. Where line w intersects line y, the angles are: 9, 12, 11, 10.
What is m∠2?
°

What is m∠1?

Answer 1

To solve for the angles, we can use the properties of transversals cutting parallel lines.

1. **At the intersection of line x and line z:**
- The angles are labeled clockwise as:
- ∠1
- ∠4
- ∠3
- ∠2

Given that these angles form a pair of vertical angles, we have that:
- ∠1 + ∠2 = 180° (they are same-side interior angles)
- ∠3 + ∠4 = 180° (they are also same-side interior angles)

Since the angles are:
- ∠1 + ∠4 = 180°
- ∠2 + ∠3 = 180°

2. **At the intersection of line w and line z:**
- The angles are labeled as:
- ∠5
- 75°
- ∠7
- ∠6

Since these lines are parallel, we can equate:
- ∠4 = 75° (alternate interior angles: ∠4 on line x + z corresponds to ∠5 on line w + z).

Thus, we find:
- Since ∠4 = 75°, we can substitute to find other angles:
- From the relationship at line x and z,
\[
\angle 1 + 75° = 180°
\]
\[
\angle 1 = 180° - 75° = 105°
\]

3. **To find m∠2:**
Using ∠1 = 105°, we can use the angle relationships:
\[
\angle 1 + \angle 2 = 180°
\]
Substituting:
\[
105° + \angle 2 = 180°
\]
\[
\angle 2 = 180° - 105° = 75°
\]

So, the values we have found are:
- **m∠1 = 105°**
- **m∠2 = 75°**