Question

Look at this diagram:

N
O
P
Q
R
S
T
U


If
OQ
and
RT
are parallel lines and mOPN= 134.1°, what is mTSP?

Answer 1

To find the measure of angle \( mTSP \), we can use the information given about the parallel lines \( OQ \) and \( RT \), along with the transversal formed by line \( PS \).

Since \( OQ \) is parallel to \( RT \), the angles formed by a transversal that intersects these lines are related through the Corresponding Angles Postulate and Alternate Interior Angles Theorem.

1. **Identify the angles**: The angle \( mOPN = 134.1^\circ \) is formed by ray \( OP \) extending towards \( O \) and ray \( PN \) extending down towards line \( OQ \).

2. **Determine the relationship**: Since \( OQ \parallel RT \) and \( OP \) acts as a transversal, angle \( OPN \) and angle \( TSP \) are alternate interior angles. Alternate interior angles are congruent when two lines are parallel.

3. **Find the measure of angle \( TSP \)**:
\[
mTSP = mOPN
\]
Therefore:
\[
mTSP = 134.1^\circ
\]

Thus, the measure of angle \( TSP \) is \( \boxed{134.1^\circ} \).