Answer:
[tex]\angle5 \cong \angle 3[/tex] by alternate interior angles theorem.
[tex]m\angle 8+120^{o}=180^{o}[/tex]; Substitution property of equality.
Step by step explanation:
We have been given that line m is parallel to line in our given diagram and measure of ∠3 is 120°.
Step 1. We have been given that m∥n and m∠3=120°.
Step 2. Since we know that alternate interior angles formed by a transversal cutting two parallel lines are congruent.
We can see from our graph that angle 3 and angle 5 is on the opposite sides of transversal and inside our parallel lines, therefore, ∠5≅∠3 by alternate interior angles theorem.
Step 3. By the definition of angle congruence, m∠5=m∠3.
Step 4. We have seen that measure of angle 5 equals to measure of 3 and we are given that m∠3 equals 120°, therefore, by substitution property of equality [tex]m\angle 5=120^{o}[/tex].
Step 5. We can see that angle 8 and angle 5 form a linear pair of angles, therefore, [tex]m\angle 8+m\angle 5=180^{o}[/tex].
Step 6. Upon substituting measure of angle 5 in linear pair angles equation we will get,
[tex]m\angle 8+120^{o}=180^{o}[/tex]
Therefore, by substitution property of equality [tex]m\angle 8+120^{o}=180^{o}[/tex].
Step 7. Subtraction property of equality states that we can subtract same quantity from both sides of an equation, therefore, by subtracting 120 degrees from both sides of our equation we will get [tex]m\angle 8=60^{o}[/tex].
