Question
If PR and SU are parallel lines and mPQO = 60°, what is mSTQ?
Answers
GPT-4o mini
To solve this problem, let's first set up what we know:
1. PR and SU are parallel lines.
2. The measure of angle PQO (denoted as \( mPQO \)) is 60°.
Given that PR and SU are parallel lines, we can use properties of angles formed by a transversal cutting through the parallel lines to determine the measure of angle STQ (denoted as \( mSTQ \)).
Assuming that line QO acts as a transversal intersecting the parallel lines PR and SU, then:
- With PR and SU being parallel, angle PQO and angle STQ are alternate interior angles.
- Alternate interior angles are equal when two lines are parallel.
Since we know that \( mPQO = 60° \), we can conclude that:
\[
mSTQ = mPQO = 60°
\]
Therefore, \( mSTQ \) is also \( 60° \).
1. PR and SU are parallel lines.
2. The measure of angle PQO (denoted as \( mPQO \)) is 60°.
Given that PR and SU are parallel lines, we can use properties of angles formed by a transversal cutting through the parallel lines to determine the measure of angle STQ (denoted as \( mSTQ \)).
Assuming that line QO acts as a transversal intersecting the parallel lines PR and SU, then:
- With PR and SU being parallel, angle PQO and angle STQ are alternate interior angles.
- Alternate interior angles are equal when two lines are parallel.
Since we know that \( mPQO = 60° \), we can conclude that:
\[
mSTQ = mPQO = 60°
\]
Therefore, \( mSTQ \) is also \( 60° \).