Question

two parallel lines are cut by a transversal as shown below. suppose $m\angle5 = 79^\circ$. find $m\angle2$ and $m\angle3$.

Explanation:

Step1: Find \( m\angle2 \)

\(\angle2\) and \(\angle5\) are corresponding angles (since two parallel lines are cut by a transversal, corresponding angles are equal). So \( m\angle2 = m\angle5 \).
Given \( m\angle5 = 79^\circ \), then \( m\angle2 = 79^\circ \).

Step2: Find \( m\angle3 \)

\(\angle2\) and \(\angle3\) are supplementary angles (they form a linear pair, so their sum is \( 180^\circ \)). So \( m\angle2 + m\angle3 = 180^\circ \).
We know \( m\angle2 = 79^\circ \), so \( m\angle3 = 180^\circ - 79^\circ = 101^\circ \).

Answer:

\( m\angle2 = \boldsymbol{79}^\circ \)
\( m\angle3 = \boldsymbol{101}^\circ \)