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. ∠1 and the 120° angle are vertical angles. So, m∠1 = 120°. Justification: Vertical - Angles Theorem.

Step2: Identify linear - pair relationship

∠1 and ∠2 form a linear pair. A linear pair of angles is supplementary (sum to 180°). So, m∠2=180 - 120 = 60°. Justification: Linear - Pair Postulate.

Step3: Identify vertical - angles relationship again

∠2 and ∠3 are vertical angles. So, m∠3 = m∠2 = 60°. Justification: Vertical - Angles Theorem.

Step4: Identify vertical - angles relationship for ∠4

∠4 and the other 120° angle are vertical angles. So, m∠4 = 120°. Justification: Vertical - Angles Theorem.

Answer:

Measure	Justification
m∠2 = 60°	Linear - Pair Postulate
m∠3 = 60°	Vertical - Angles Theorem
m∠4 = 120°	Vertical - Angles Theorem