Question

I’m confused on how to find the angle measures of 1, 2, and 3? Then, I have to explain my reasoning using the different theorems such as alternate exterior theorem, interior theorem, corresponding theorem, etc.

Answer 1

Recall that with parallel lines, the following angles are congruent:

Now, two angles are called alternate exterior angles if they are on opposite sides of the transversal line in different lines as shown on the following diagram:

the colors indicate the alternate exterior angles pairs.

Answer:

Since the vertical lines are parallel, then by the alternate exterior angles theorem we know that:

`\measuredangle2=102^(\circ).`

Now, angles 2 and 3 are supplementary, which means that they add up to 180 degrees:

`\measuredangle2+\measuredangle3=180^(\circ).`

Substituting ∡2=102 degrees and solving for ∡3 we get:

`\measuredangle3=180^(\circ)-102^(\circ)=78^(\circ).`

Finally, the angle given and angle 1 are alternate interior angles, therefore:

`\measuredangle1=102^(\circ).`