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

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

Step2: Identify vertical - angles for $\angle2$

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

Step3: Identify linear - pair for $\angle3$

$\angle3$ and the $120^{\circ}$ angle form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, $m\angle3 = 180 - 120=60^{\circ}$. Justification: Linear - Pair Postulate.

Step4: Identify linear - pair for $\angle4$

$\angle4$ and the $122^{\circ}$ angle form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, $m\angle4=180 - 122 = 58^{\circ}$. Justification: 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