1. Since AB is parallel to DC, and BC is a transversal, ∠ABC and ∠C are alternate interior angles. Since alternate interior angles are congruent ∠ABC=∠C, so ∠C=118°. Now, ∠n and ∠C are supplementary, so: ∠n+∠C=180° ∠n+118°=180° ∠n=180°-118° ∠n=62° We can conclude that the measure of angle n is 62°
2. Angle p and angle n are vertical angles, which means they are opposite angles made by the two intersecting lines BC and DC. Since vertical angles are congruent, ∠p=∠n. Since angle ∠n=62° and ∠n=∠p, ∠p=62° We can conclude that the measure of angle p is 62°
3. Angle q and angle C are vertical angles, which means they are opposite angles from their vertex. We now know that vertical angles are congruent, so ∠q=∠C. We also know form previous calculations that ∠C=118°. Since ∠C=∠q, ∠q=118° We can conclude that the measure of angle q is 118°
4. Notice that angle v and the angle whose measure is 96° are supplementary angles, which mean they add to 180°, so to find the measure of angle v, we just need to subtract 96° from 180°: ∠v=180°-96° ∠v=84° We can conclude that the measure of angle v is 96°
5. Just like before, angle w and the angle whose measure is 42° are supplementary, which means they add to 180°, so, just like before, to find the measure of angle v, we just need to subtract 42° from 180°: ∠w=180°-42° ∠w=138° We can conclude that the measure of angle w is 138°
According to the Corresponding Angles (CA) postulate, if two parallel lines (AB and DC in this case) are cut by a transversal (BC in this case), the corresponding angles are congruent.
Now ∠ABC is 118°, and its corresponding angle is ∠q, so this means that ∠q is 118° also.
∠q is supplementary to ∠n which means that they both create a straight line. So in other words, the sum of both angles is equal to 180°. So to get ∠n just subtract ∠q from 180°.
∠n = 180°-118° = 62°
According to the vertical angles postulate, vertical angles are congruent. ∠n and ∠p are vertical angles, so they are congruent.
∠n = 62° and ∠p = 62°
∠v is supplementary to the angle that is measured as 96°. To get ∠v subtract 96° from 180°.
∠v = 180°-96° = 84°
Lastly, ∠w is supplementary to the angle that is measured as 42°. To get that, all you need to do is subtract 42° from 180°. ∠w = 180°-42°= 138°
