Question

Lines ℓ and m are intersected by transversal t. ℓ ∥ m.

There are two parallel horizontal lines l and m intersected by another line t making angles 1 and 3 with l and 5, 7 with m. 1 ,4 and 2 , 3 are opposite angles at the point of intersection of l and t. 5, 8 and 6, 7 are opposite angles at the point of intersection of m and t.


If m∠3 = 78°, what is m∠6?

Answer 1

m<6 = 78°

Explanation:

I hope your drawing of this problem looks somewhat like this:

^ t

/

/

1 / 2

<-----------------------------------------------------------------------------> ℓ

3 / 4

/

5 / 6

<------------------------------------------------------------------------------> m

7 / 8

/

/

V

Sorry about the terrible drawing, but I hope I got the angle numbers correctly written.

Angles 3 and 6 are are called alternate interior angles.

They are "interior angles" because they are on the inside of lines l and m. They are "alternate angles" because they are on different sides of the transversal, t.

There is a Geometry theorem about this situation.

Theorem:

If parallel lines are cut by a transversal, then alternate interior angles are congruent.

In this case, since the pair of angles 3 and 6 is a pair of alternate interior angles, then by the theorem above, they are congruent.

m<6 = m<3

Since m<3 = 78°, then m<6 = 78°.