Question

parallel lines cut by a transversal
identify the types of angles. all horizontal lines are parallel.
if ( t parallel s ) and ( mangle 2 = 97^circ ), ( mangle 6 = 83^circ ), find:
( mangle 3 = )
( mangle 10 = )
( mangle 9 = )
( mangle 5 = )
( mangle 7 = )
( mangle 16 = )

Explanation:

Step1: Find \( m\angle3 \)

\(\angle2\) and \(\angle3\) are supplementary (linear pair), so \( m\angle3 = 180^\circ - m\angle2 \).
\( m\angle3 = 180^\circ - 97^\circ = 83^\circ \)

Step2: Find \( m\angle5 \)

\(\angle2\) and \(\angle5\) are same - side interior angles? Wait, no, since \( t\parallel s \), \(\angle2\) and \(\angle5\) are supplementary? Wait, actually, \(\angle6 = 83^\circ\), and \(\angle5\) and \(\angle6\) are supplementary? Wait, no, let's correct. \(\angle2\) and \(\angle5\): since \( t\parallel s \), \(\angle2\) and \(\angle5\) are same - side interior angles? Wait, no, \(\angle2 = 97^\circ\), \(\angle6 = 83^\circ\). \(\angle5\) and \(\angle6\) are adjacent? Wait, maybe \(\angle5\) and \(\angle2\) are corresponding? Wait, no, let's use the fact that \(\angle3 = 83^\circ\), and \(\angle5\) is equal to \(\angle3\) (alternate interior angles) because \( t\parallel s \). So \( m\angle5 = 83^\circ \)

Step3: Find \( m\angle10 \)

\(\angle2 = 97^\circ\), and \(\angle10\) is equal to \(\angle2\) (corresponding angles) because \( t\parallel s \), so \( m\angle10 = 97^\circ \)

Step4: Find \( m\angle7 \)

\(\angle6 = 83^\circ\), and \(\angle7\) is supplementary to \(\angle6\) (linear pair), so \( m\angle7 = 180^\circ - 83^\circ = 97^\circ \)

Step5: Find \( m\angle9 \)

\(\angle9\) is equal to \(\angle6\) (alternate interior angles) because \( t\parallel s \), so \( m\angle9 = 83^\circ \)

Step6: Find \( m\angle16 \)

Assuming the lines are parallel, \(\angle16\) is equal to \(\angle2\) (corresponding angles) or \(\angle10\). Since \( m\angle10 = 97^\circ \), \( m\angle16 = 97^\circ \) (assuming the transversal and parallel lines structure)

Answer:

\( m\angle3 = 83^\circ \), \( m\angle5 = 83^\circ \), \( m\angle10 = 97^\circ \), \( m\angle7 = 97^\circ \), \( m\angle9 = 83^\circ \), \( m\angle16 = 97^\circ \)