Angle Measures: ∠3 = 95^(∘), ∠4=85^(∘) Explanation: See solution.
Practice makes perfect
Let's consider the given diagram.
To find the measure of ∠ 3, we will use the fact that corresponding angles of parallel lines are congruent. Since the 95^(∘) angle and ∠ 3 are corresponding angles and lines a and b are parallel, these angles are congruent.
Congruent angles have the same measure, so the measure of ∠ 3 is 95^(∘). Finally, note that ∠ 4 and ∠ 3 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 ∠ 4.
m∠ 4+ 95^(∘)=180^(∘)
⇕
m∠ 4=85^(∘)
