Asked by khan
If
LN
and
OQ
are parallel lines and mQPR= 124°, what is mOPR?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find \( mOPR \) given that lines \( LN \) and \( OQ \) are parallel, and \( mQPR = 124^\circ \), we can use the properties of parallel lines and angles formed by a transversal.
Since \( OQ \) is a transversal line that intersects the parallel lines \( LN \) and the measure of angle \( QPR \) is given as \( 124^\circ \), we can find \( mOPR \) using the concept of corresponding angles or alternate interior angles.
1. **Identify angles**: Angle \( QPR \) and angle \( OPR \) are corresponding angles since \( OQ \) (the transversal) intersects the parallel lines \( LN \) and \( OQ \).
2. **Use properties of parallel lines**: Corresponding angles are equal when a transversal intersects parallel lines.
Therefore,
\[
mOPR = mQPR = 124^\circ
\]
Thus, \( mOPR = 124^\circ \).
Since \( OQ \) is a transversal line that intersects the parallel lines \( LN \) and the measure of angle \( QPR \) is given as \( 124^\circ \), we can find \( mOPR \) using the concept of corresponding angles or alternate interior angles.
1. **Identify angles**: Angle \( QPR \) and angle \( OPR \) are corresponding angles since \( OQ \) (the transversal) intersects the parallel lines \( LN \) and \( OQ \).
2. **Use properties of parallel lines**: Corresponding angles are equal when a transversal intersects parallel lines.
Therefore,
\[
mOPR = mQPR = 124^\circ
\]
Thus, \( mOPR = 124^\circ \).
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