How to solve for x in parallel planes?..?

Question

Solve for x when m ll L, m<1=2x+44 and m<5=5x+38

http://i261.photobucket.com/albums/ii66/questionasker810/plane2.jpg


ll means parallel, just in case you don't know :)

~Please show how you got the answer thankes!

Answer 1

m<1=2x+44 and m<5=5x+38
Sorry, but I do not understand your notation. Are you sure it should look like this?

Cheers,

Kempos

Answer 2

If "m<1" means the measure of angle 1 and "m<5" the measure of angle 5, and if M || L - I will change the name for plane m to a capital, to make the notation less confusing. It is readily apparent that we are looking at all three planes edge-on, the projection of them becoming two parallel lines cut by a transversal. We may then use our Euclidian plane geometry to show that
m<1 = m<5 by the geometric theorem of corresponding angles of a transversal and parallel lines. Because the measures of these angles are equal, what each is equal to would be equal to each other. In other words,
2x + 44 = 5x + 38

This is a simple linear algebraic equation that becomes
6 = 3x
or x = 2.

Answer 3

We have two parallel lines cut by a transversal.

Angle 1 = Angle 5 by corresponding angles.

Therefore

2x + 44 = 5x + 38
6 = 3x
x = 2