Question

tell why each of the angles indicated are congruent to the a
m||n
∠3:
∠4:
∠7:

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are congruent. $\angle1$ and $\angle3$ are vertical angles. Since $\angle1 = 45^{\circ}$, $\angle3=45^{\circ}$ because vertical angles have equal measures.

Step2: Identify corresponding - angle relationship

Corresponding angles are congruent when two parallel lines are cut by a transversal. $\angle1$ and $\angle4$ are corresponding angles with $m\parallel n$ and $t$ as the transversal. So $\angle4 = 45^{\circ}$ as corresponding angles have equal measures.

Step3: Identify alternate - exterior - angle relationship

Alternate exterior angles are congruent when two parallel lines are cut by a transversal. $\angle1$ and $\angle7$ are alternate exterior angles with $m\parallel n$ and $t$ as the transversal. So $\angle7 = 45^{\circ}$ as alternate exterior angles have equal measures.

Answer:

$\angle3$: Vertical angles are congruent.
$\angle4$: Corresponding angles are congruent.
$\angle7$: Alternate exterior angles are congruent.