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 congruent. Angle 1 and the given $44^{\circ}$ angle are vertical angles. So $m\angle1 = 44^{\circ}$.

Step2: Identify linear - pair relationship

Angle 1 and angle 2 form a linear pair. A linear pair of angles is supplementary (sum to $180^{\circ}$). So $m\angle2=180 - 44=136^{\circ}$.

Step3: Identify vertical - angle relationship for angle 3

Angle 2 and angle 3 are vertical angles. Since vertical angles are congruent, $m\angle3 = 136^{\circ}$.

Step4: Identify vertical - angle relationship for angle 4

Angle 4 and the given $44^{\circ}$ angle are vertical angles. So $m\angle4 = 44^{\circ}$.

Answer:

Measure	Justification
$m\angle2 = 136^{\circ}$	Linear - pair angles are supplementary
$m\angle3 = 136^{\circ}$	Vertical angles are congruent
$m\angle4 = 44^{\circ}$	Vertical angles are congruent