Question

find the measures of the numbered angles in the figure, shown to the right. name the theorem that justifies each answer. complete the table below. measure justification m∠1 = m∠2 = m∠3 = m∠4 =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Since $\angle1$ and the given $70^{\circ}$ angle are vertical angles, $m\angle1 = 70^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle1$ and $\angle2$ are corresponding angles. For parallel lines (indicated by the arrow - heads), corresponding angles are equal. So $m\angle2=70^{\circ}$.

Step3: Identify vertical - angle relationship for $\angle3$

$\angle2$ and $\angle3$ are vertical angles. Vertical angles are equal, so $m\angle3 = 70^{\circ}$.

Step4: Identify corresponding - angle relationship for $\angle4$

$\angle1$ and $\angle4$ are corresponding angles for the parallel lines. So $m\angle4 = 70^{\circ}$.

Answer:

$m\angle1 = 70^{\circ}$, $m\angle2 = 70^{\circ}$, $m\angle3 = 70^{\circ}$, $m\angle4 = 70^{\circ}$