Question: Triangle with Variable Angles

Yes it can. Give it a try :-)

Great question!

Let's consider the following analogous question:

Ann and Bob have a COMBINED age of 60.
So, if x = Ann's age, then 60-x = Bob's age
At this point, we cannot yet determine the value of x.
We need a SECOND piece of information.
Notice that it doesn't help to REUSE the same information about the sum of their ages.

To see what I mean, let's REUSE the same information about the sum of their ages.
(Ann's age) + (Bob's age) = 60
So, (x) + (60 - x) = 60
Simplify to get 60 = 60 [this doesn't help us]

The same problem occurs in your solution; you're trying to use the same information twice.

First, you used the fact that angles on a line add to 180 degrees in order to determine that the other angle is [180-(4x+70)]

Then you used the SAME principle (angles on a line add to 180), and you used the SAME two angles. Since we are reusing the same information, we don't advance the solution.

Does that help?

Cheers,
Brent

The mistake here is that you are assigning the SAME variable, y, to two DIFFERENT angles.
We can't do this since we aren't told that those two angles are equal.