Question: Triangle with Variable Angles

Comment on Triangle with Variable Angles

can this question be solved by using exterior sum angle property of triangle?
gmat-admin's picture

Yes it can. Give it a try :-)


Why does (4x+70) + [180-(4x+70)] = 180 not work? Since the sum of angles on a line is 180

I keep getting zero which seems to be the solution to this equation.

gmat-admin's picture

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?


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