Find the measures of all angles formed by line a parallel to line b with transversal m, if:

a
one of the angles is 77°

To find the measures of all angles formed by line a parallel to line b with transversal m, given that one of the angles is 77°, we can make use of the properties and relationships of parallel lines and transversals.

First, let's understand the relationship of parallel lines and transversals. When a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the alternate exterior angles are congruent.

Since one of the angles formed is already given as 77°, we can use this information to find the measures of the other angles. Let's label the angles for clarity:

Angle 1 = 77° (given)
Angle 2 (corresponding angle to Angle 1)
Angle 3 (alternate interior angle to Angle 1)
Angle 4 (alternate exterior angle to Angle 1)

Now, since Angle 2 is the corresponding angle to Angle 1, they are congruent. Therefore, Angle 2 also measures 77°.

Similarly, Angle 3 is the alternate interior angle to Angle 1, and alternate interior angles are congruent. Therefore, Angle 3 also measures 77°.

Lastly, Angle 4 is the alternate exterior angle to Angle 1, and alternate exterior angles are congruent. Therefore, Angle 4 also measures 77°.

To summarize, the measures of all angles formed by line a parallel to line b with transversal m are as follows:
Angle 1 = 77°
Angle 2 = 77°
Angle 3 = 77°
Angle 4 = 77°

think of alternate and corresponding angles. You've seen this diagram dozens of times already.