Question

two parallel lines are cut by a transversal as shown below. suppose m ∠7 = 48°. find m ∠2 and m ∠4. m ∠2 = \boxed{}° m ∠4 = \boxed{}°

Explanation:

Step1: Find \( m\angle 2 \)

\(\angle 2\) and \(\angle 7\) are corresponding angles (since two parallel lines cut by a transversal, corresponding angles are equal). Given \( m\angle 7 = 48^\circ \), so \( m\angle 2 = 48^\circ \).

Step2: Find \( m\angle 4 \)

\(\angle 2\) and \(\angle 4\) are supplementary angles (they form a linear pair, so their sum is \( 180^\circ \)). We know \( m\angle 2 = 48^\circ \), so \( m\angle 4 = 180^\circ - 48^\circ = 132^\circ \).

Answer:

\( m\angle 2 = \boldsymbol{48}^\circ \)
\( m\angle 4 = \boldsymbol{132}^\circ \)