To find the measure of ∠ 3, we will use the fact that vertical angles are congruent. Since ∠ 3 and the 35^(∘) angle are formed on opposite sides of the point of intersection, they are vertical angles and are congruent.
Congruent angles have the same measure, so the measure of ∠ 3 is 35^(∘). Note that ∠ 3 and ∠ 1 form a straight line.
Therefore, they are supplementary and the sum of their measures is 180^(∘). With this information, we can find the measure of ∠ 1.
m∠ 1+ 35^(∘)=180^(∘)
⇕
m∠ 1=145^(∘)
Let's now find the measure of ∠ 2. Because ∠ 2 and ∠ 1 are formed on opposite sides of the point of intersection they are vertical angles and are congruent.
Congruent angles have the same measure, so the measure of ∠ 2 is 145^(∘). To find the measures of the remaining angles, we will use the fact that corresponding angles of parallel lines are congruent. Lines l and m are cut by a transversal t creating four angles around each point of intersection. Let's match the corresponding angles into pairs.
From the graph above we can see that the following pairs of angles are corresponding.
∠ 1 and ∠ 5
∠ 2 and ∠ 6
∠ 3 and ∠ 7
∠ 8 and ∠ 4
Finally, using the information we already found and the fact that corresponding angles are congruent we can find the measures of the missing angles.
∠ 4 = 35^(∘)
∠ 5 = 145^(∘)
∠ 6 = 145^(∘)
∠ 7 = 35^(∘)
