Angle Measures: ∠5 = 49^(∘), ∠6=131^(∘) Explanation: See solution.
Practice makes perfect
Let's consider the given diagram.
To find the measure of ∠ 5, we will use the fact that corresponding angles of parallel lines are congruent. Since the 49^(∘) angle and ∠ 5 are corresponding angles and lines a and b are parallel, these angles are congruent.
Congruent angles have the same measure, so the measure of ∠ 5 is 49^(∘). Finally, note that ∠ 5 and ∠ 6 form a straight line.
Therefore, they are supplementary and the sum of their measures is 180^(∘). With this information, we can finally find the measure of ∠ 6.
m∠ 6+ 49^(∘)=180^(∘)
⇕
m∠ 6=131^(∘)
