Question

two parallel lines are cut by a transversal as shown below. suppose m∠8 = 104°. find m∠1 and m∠3.

Explanation:

Step1: Identify vertical - angle relationship

$\angle 3$ and $\angle 8$ are vertical angles. Vertical angles are congruent. So $m\angle3 = m\angle8$.

Step2: Determine the measure of $\angle 3$

Since $m\angle8 = 104^{\circ}$, then $m\angle3=104^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle 1$ and $\angle 3$ are supplementary angles (linear - pair). The sum of the measures of supplementary angles is $180^{\circ}$. So $m\angle1 + m\angle3=180^{\circ}$.

Step4: Calculate the measure of $\angle 1$

$m\angle1=180^{\circ}-m\angle3$. Substitute $m\angle3 = 104^{\circ}$ into the equation. Then $m\angle1 = 180 - 104=76^{\circ}$.

Answer:

$m\angle1 = 76^{\circ}$
$m\angle3 = 104^{\circ}$