Question

given ( l parallel m ), cut by transversal ( t ); ( mangle6 = 130^{circ} ) prove ( mangle3 = 130^{circ} ) statements 1. ( l parallel m ), cut by transversal ( t ); ( mangle6 = 130^{circ} ) 2. ( angle3 ) and ( angle6 ) are alternate interior angles. 3. ( angle3congangle6 ) 4. ( mangle3 = mangle6 ) 5. reasons 1. given 2. def. of alt. interior ( angle s ) 3. 4. def. of ( congangle s ) 5. substitution a ( mangle3 = 130^{circ} ) b. ( angle3congangle7 ) c. corresponding angles postulate d. alternate interior angles theorem

Explanation:

Step1: Identify the theorem for alternate interior angles

When two parallel lines are cut by a transversal, alternate interior angles are congruent. This is the Alternate Interior Angles Theorem.

Step2: Substitute the measure of ∠6

Since \(m\angle6 = 130^{\circ}\) and \(m\angle3=m\angle6\) (from the congruence of alternate - interior angles), by substitution, \(m\angle3 = 130^{\circ}\)

Answer:

d. Alternate Interior Angles Theorem; \(m\angle3 = 130^{\circ}\)