Question

Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?



Angle 2 =
°



Angle 3 =
°



Angle 4 =
°

Answer 1

To find the measures of angles 2, 3, and 4 given that angle 1 is 110° and the lines m || n and q || p, we can use the properties of parallel lines and transversals.

1. **Lines m and n are parallel**:
- When two parallel lines are intersected by a transversal, corresponding angles are equal, and alternate interior angles are equal.

2. **Lines q and p are parallel**:
- Similarly, for the other pair of parallel lines, corresponding and alternate interior angles also hold.

### Step 1: Analyze Angle 1

Angle 1 is given as 110° at the intersection of line q and line m. Since lines m and n are parallel, angle 1 corresponds with angle 4 (the upper right angle at line q and line n).

- Therefore:
\[
\text{Angle 4} = \text{Angle 1} = 110°
\]

### Step 2: Find Angle 2

Angle 2 is located at the intersection of line p and line m. Since lines p and q are parallel, angle 2 must be congruent to angle 1 (as they are alternate interior angles).

- Therefore:
\[
\text{Angle 2} = \text{Angle 1} = 110°
\]

### Step 3: Find Angle 3

Angle 3 is located at the intersection of line p and line n. Since we have already established that lines m and n are parallel, angle 3 is the same as angle 4 (as they are corresponding angles).

- Therefore:
\[
\text{Angle 3} = \text{Angle 4} = 110°
\]

### Summary of Angle Measures

- Angle 2 = **110°**
- Angle 3 = **110°**
- Angle 4 = **110°**

Thus, the measures are:

- Angle 2 = 110°
- Angle 3 = 110°
- Angle 4 = 110°