Question

two parallel lines are cut by a transversal as shown below. suppose m∠5 = 97°. find m∠2 and m∠3. m∠2 = □° m∠3 = □°

Explanation:

Step1: Identify relationship for ∠2

∠2 and ∠5 are corresponding angles (parallel lines, transversal), so \( m\angle2 = m\angle5 \). Given \( m\angle5 = 97^\circ \), thus \( m\angle2 = 97^\circ \).

Step2: Identify relationship for ∠3

∠2 and ∠3 are supplementary (linear pair), so \( m\angle2 + m\angle3 = 180^\circ \). Substitute \( m\angle2 = 97^\circ \): \( 97^\circ + m\angle3 = 180^\circ \), so \( m\angle3 = 180^\circ - 97^\circ = 83^\circ \).

Answer:

\( m\angle2 = \boldsymbol{97}^\circ \)
\( m\angle3 = \boldsymbol{83}^\circ \)