It is given that m∠ 4=101^(∘). Using this information, we need to find the measure of angle ∠ 6. We will use the given diagram to identify these angles. We can name the lines n and m for the following explanations to be more clear to follow as we proceed.
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
According to the theorem, angles ∠ 4 and ∠ 6 are congruent and have the same measures. Therefore, we can write that m∠ 6=101^(∘).
m∠ 4 = 101^(∘) and m∠ 4 = m∠ 6
⇓
m∠ 6 = 101^(∘)
Extra
Further Explanation
Notice that since ∠ 3 and ∠ 5 also lie on opposite sides of the transversal t and on the interior sides of the parallel lines n and m, these angles are the alternate interior angels as well.
