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 3 =
°



Angle 4 =
°

Answer 1

To determine the measures of angles 2 and 3 such that lines \( m \parallel n \) and \( q \parallel p \), we can use the properties of parallel lines and corresponding angles.

- Since \( m \parallel n \) and \( q \) intersects both, angles formed by this intersection will be corresponding angles. Specifically, we have:
- Angle \( 1 \) (which is given as \( 110^\circ \)) and angle \( 4 \) are corresponding angles.

Therefore:
\[
\text{Angle } 4 = \text{Angle } 1 = 110^\circ
\]

Now for angle \( 3 \) at the intersection of line \( p \) and line \( n \):
- Since \( p \) intersects \( n \) and \( m \) is parallel to \( n \), we know that angle \( 3 \) and angle \( 2 \) are also corresponding angles.
- This means if we assume angle \( 2 \) is formed in relation to angle \( 1 \), we can calculate angle \( 2 \):
- Since angle \( 1 \) (which is \( 110^\circ \)) and angle \( 2 \) are in a linear pair formed by line \( p \), we can find angle \( 2 \) using the following:
\[
\text{Angle } 2 = 180^\circ - \text{Angle } 1
\]
\[
\text{Angle } 2 = 180^\circ - 110^\circ = 70^\circ
\]

Since angle \( 3 \) is also a corresponding angle to angle \( 2 \), we also have:
\[
\text{Angle } 3 = \text{Angle } 2 = 70^\circ
\]

To summarize, we find:
\[
\text{Angle } 3 = 70^\circ
\]
\[
\text{Angle } 4 = 110^\circ
\]

Thus:
\[
\text{Angle 3} = 70^\circ
\]
\[
\text{Angle 4} = 110^\circ
\]