In the illustration (in the link below), suppose l ∥ m and ∠1 = 55°. What are the measures of the other angles?

www.webassign.net/ewenmath10/12-1-013.gif

∠2 = °
∠3 = °
∠4 = °

angle2 is 55 degrees because it is vertically opposite angle 1. Angles 2 and 3 are corresponding thus making them the same. And angle 4 is supplementary to angle 3 thus making it 180 degrees - 55 degrees : )

thank you!

To find the measures of the other angles in the given illustration, which shows two parallel lines intersected by a transversal, we need to apply some angle relationships.

First, since line l is parallel to line m, we can use the alternate interior angles theorem. This theorem states that when a transversal intersects two parallel lines, the alternate interior angles are congruent.

In the given illustration, ∠1 and ∠2 are alternate interior angles. It is given that ∠1 = 55°, so ∠2 will also be 55°.

Next, we can consider the corresponding angles formed by the transversal and the parallel lines. Corresponding angles, when a transversal intersects two parallel lines, are also congruent.

In the illustration, ∠2 and ∠3 are corresponding angles. Since we found that ∠2 = 55°, ∠3 will also be 55°.

Lastly, we can find ∠4 by considering the angles opposite to ∠3. By the vertical angles theorem, vertical angles are congruent.

In the illustration, ∠3 and ∠4 are vertical angles. Since ∠3 = 55°, ∠4 will also be 55°.

Therefore, the measures of the other angles are:
∠2 = 55°
∠3 = 55°
∠4 = 55°