30 point

in the following diagram, line l and line m are parallel to each other. line t is a transversal intersect line l and line m.

a student named alex is asked to solve for the degree measure of angle 4, given that the measure of angle 6 is 40°. alex tells the teacher that the m∠4 = 40°.

explain alex's mistake. in your explanation, be sure to include the key terms "corresponding angles", “parallel lines”, and "transversal" in your explanation.

b. calculate the correct measure of angle 4.

The answer to your question is:  ∠4 = 140°

Step-by-step explanation:

If there are two parallel lines cut by a transversal line 8 angles are formed.

These angles are classified as corresponding angles, alternate exterior angles, alternate interior angles and same-side angles.

Alternate exterior angles measure the same. Also alternate interior angles measure the same.

Same-side angles are supplementary angles, that means that their sum gives 180°.

Finally corresponding angles measure the same.

In the figure we notice that angles 6 and 8 are same side angles, so:

                                    ∠6 + ∠8 = 180

and ∠6 = 40°               40 + ∠8 = 180

                                   ∠8 = 180 - 40

                                   ∠8 = 140°

and ∠4 and ∠8 are corresponding angles so,

                       ∠4 = ∠8 = 140°