Question

two parallel lines are cut by a transversal as shown below. suppose m∠6 = 43°. find m∠1 and m∠3.

Explanation:

Step1: Identify angle - relationship for ∠1 and ∠6

∠1 and ∠6 are alternate - exterior angles. When two parallel lines are cut by a transversal, alternate - exterior angles are congruent.
$m\angle1=m\angle6$

Step2: Substitute the value of ∠6

Since $m\angle6 = 43^{\circ}$, then $m\angle1=43^{\circ}$

Step3: Identify angle - relationship for ∠3 and ∠6

∠3 and ∠6 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.
$m\angle3=m\angle6$

Step4: Substitute the value of ∠6

Since $m\angle6 = 43^{\circ}$, then $m\angle3=43^{\circ}$

Answer:

$m\angle1 = 43^{\circ}$
$m\angle3 = 43^{\circ}$