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 m∠1 = m∠2 = m∠3 = m∠4 = justification

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. ∠1 and the 103° angle are vertical angles, so $m\angle1 = 103^{\circ}$.

Step2: Use linear - pair relationship

∠1 and ∠2 form a linear pair. The sum of angles in a linear pair is 180°. So $m\angle2=180 - 103=77^{\circ}$.

Step3: Identify vertical - angle relationship again

∠2 and ∠3 are vertical angles. So $m\angle3 = 77^{\circ}$.

Step4: Use linear - pair relationship for ∠3 and ∠4

∠3 and ∠4 form a linear pair. So $m\angle4=180 - 77 = 103^{\circ}$.

Answer:

$m\angle1 = 103^{\circ}$, Justification: Vertical - angles theorem
$m\angle2 = 77^{\circ}$, Justification: Linear - pair postulate
$m\angle3 = 77^{\circ}$, Justification: Vertical - angles theorem
$m\angle4 = 103^{\circ}$, Justification: Linear - pair postulate