Question

Can someone explain this simple geometry problem to me ? Will Medal/Fan.

Answer 1

You have parallel lines.
With parallel lines cut by a transversal, alternate interior angles are congruent.

Answer 2

could you dumb that down ?

Answer 3

I know the answer is 40, but i want to know how it works.

Answer 4

Ok, I'll explain it in more detail.
Look above at the figure.
There are two lines, m and n, both intersected by line t.

Answer 5

Okay, I will wait until you finish to reply.

Answer 6

When two lines are intersected in two different points by a third line, the third line is called a transversal.
Since line t intersects lines m and n in two different points, line t is a transversal to lines m and n.

Answer 7

Now let's say that lines m and n are parallel lines.
Notice you have parallel lines in your problem, so you will see soon how this relates to your problem.

Answer 8

This is a theorem:
If two parallel lines are cut (meaning intersected) by a transversal, then alternate interior angles are congruent.

Answer 9

Alternate interior angles are angles that are both on the inside of the two parallel lines, and are on different sides of the transversal.
I'll show it to you in the figure below.

Answer 10

Above, all angles 1, 2, 3, and 4 are interior angles.
Angles 1 and 4 are alternate interior angles.
Angles 2 and 3 are alternate interior angles.
If we are told that the lines m and n are parallel, then by the theorem above we can state that
angles 1 and 4 are congruent
angles 2 and 3 are congruent
since in each case above we are dealing with a pair of alternate interior angles.

Answer 11

Now we can go back to your problem.

Answer 12

In your figure, look at lines l and m.
They are parallel.
That means that alternate interior angles formed by these two lines and a transversal are congruent.

Answer 13

Now look at angles 5 and 2.
The left side of the triangle that connects lines l and m is a transversal.
Lines l and m are parallel.
Angles 5 and 2 are alternate interior angles, so angles 5 and 2 are congruent. They have the same measure.

Answer 14

If we can find the measure of angle 2, we will know the measure of angle 5 since the two measures are equal.

Answer 15

Now look at the bottom left corner of the triangle where you see angles 1 and 2.

Answer 16

We are told that the measure of angle 1 is 140 degrees.

Answer 17

Angles 1 and 2 form a straight line.
Two angles that are adjacent that form a straight line are called a linear pair and add up to 180 degrees.
Then we have
m<1 + m<2 = 180
140 + m<2 = 180
m<2 = 180 - 140
m<2 = 40

Now we know that the measure of angle 2 is 40.
Since the measure of angle 5 is the same as the measure of angle 2, m<5 = 40

Answer 18

If you have any questions, just ask.

Answer 19

Thank you.

Answer 20

You're welcome.