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 - angles relationship

Vertical angles are equal. $\angle1$ and the $120^{\circ}$ angle are vertical angles. So, $m\angle1 = 120^{\circ}$ (Vertical - Angles Theorem).

Step2: Identify vertical - angles relationship

$\angle2$ and the $122^{\circ}$ angle are vertical angles. So, $m\angle2=122^{\circ}$ (Vertical - Angles Theorem).

Step3: Identify linear - pair relationship

$\angle1$ and $\angle3$ form a linear pair. A linear pair of angles is supplementary, i.e., their sum is $180^{\circ}$. So, $m\angle3 = 180 - 120=60^{\circ}$ (Linear - Pair Postulate).

Step4: Identify linear - pair relationship

$\angle2$ and $\angle4$ form a linear pair. Since they are supplementary, $m\angle4=180 - 122 = 58^{\circ}$ (Linear - Pair Postulate).

Answer:

Measure	Justification
$m\angle2 = 122^{\circ}$	Vertical - Angles Theorem
$m\angle3 = 60^{\circ}$	Linear - Pair Postulate
$m\angle4 = 58^{\circ}$	Linear - Pair Postulate