Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle 5 = 79^circ ). find ( mangle 2 ) and ( mangle 3 ).

Explanation:

Step1: Identify relationship for ∠2 and ∠5

Since the two lines are parallel and cut by a transversal, ∠2 and ∠5 are corresponding angles. Corresponding angles are equal when lines are parallel. So \( m\angle 2 = m\angle 5 \).
Given \( m\angle 5 = 79^\circ \), thus \( m\angle 2 = 79^\circ \).

Step2: Identify relationship for ∠3 and ∠2

∠2 and ∠3 are adjacent angles forming a linear pair, so their sum is \( 180^\circ \). That is \( m\angle 2 + m\angle 3 = 180^\circ \).
We know \( m\angle 2 = 79^\circ \), so substitute: \( 79^\circ + m\angle 3 = 180^\circ \).
Solve for \( m\angle 3 \): \( m\angle 3 = 180^\circ - 79^\circ = 101^\circ \).

Answer:

\( m\angle 2 = 79^\circ \), \( m\angle 3 = 101^\circ \)