Question

given m∠1 = 105°, find m∠4, m∠5, and m∠8.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles. So $m\angle4=m\angle1 = 105^{\circ}$.

Step2: Use corresponding - angle property

$\angle1$ and $\angle5$ are corresponding angles. Corresponding angles are equal when two lines are cut by a transversal. So $m\angle5=m\angle1=105^{\circ}$.

Step3: Use vertical - angle property again

$\angle5$ and $\angle8$ are vertical angles. So $m\angle8 = m\angle5=105^{\circ}$.

Answer:

$m\angle4 = 105^{\circ}$, $m\angle5 = 105^{\circ}$, $m\angle8 = 105^{\circ}$