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?


Hi Brent, if I assign y in the inside angle and add it as below but it doesn't work?

4x+y=110 -----1

3x-y=25 -----2

3x-y=25 +
gmat-admin's picture

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.

Ah I see. As I was thinking to add up or subtract the two equations later therefore try to avoid creating 3rd variables. Could you show the calculation if different variables were assigned here please? Thanks Brent
gmat-admin's picture

That approach won't work because we will end up with 2 equations with 3 variables.

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