Answers:
We see that ∠2 and ∠3 are corresponding angles
And since the lines u and v are parallel, ∠2 and ∠3 are congruent.
So, m∠3 = 150
We see that ∠1 and ∠2 are vertically opposite angles
Thus, ∠1 and ∠2 are congruent
So, m∠1 = 150
The relationship between ∠1 and ∠3 is an example of the following rule
When parallel lines are cut by a transversal, alternate interior angles are congruent.
Explanation:
The angles formed by two parallel lines and a transversal that are on the same side of the transversal and in the same position from the parallel lines are called corresponding angles. These angles have the same measure so they are also congruent.
So, we can fill the first part as:
We see that ∠2 and ∠3 are corresponding angles
And since the lines u and v are parallel, ∠2 and ∠3 are congruent.
So, m∠3 = 150
On the other hand, two opposite angles formed by two lines that cross are called vertically opposite. So, these angles have the same measure.
So, we can fill the second part as:
We see that ∠1 and ∠2 are vertically opposite angles
Thus, ∠1 and ∠2 are congruent
So, m∠1 = 150
Finally, we can fill the third part as:
The relationship between ∠1 and ∠3 is an example of the following rule
When parallel lines are cut by a transversal, alternate interior angles are congruent.
Because alternate interior angles are the angles that are inside the parallel line and on opposite sides of the transversal.
