mcm2112 wrote:

I do not see anything in the question that gets a 45-45-90 triangle. x could be equal to 40 and 2x=80, leaving y to be 60. Would that be a possibility?

Thanks!

Notice that angles in the triangle boil down to x, x and 2x. (Please refer to my explanation of the question above.)

Now taking the situation you have provided. "if x = 20 and 2x = 80 leaving y to be 60." It goes on to contradict x=y. and y=z which is the first thing we proved to begin our solution. Hence it is incorrect.

When dealing with GEOMETRY always look closely at the figure and find out all the values and cases you can without breaking any rule.

1. Opposite angles formed by two straight lines at vertex are equal.

2. Sum of all three angles is 180.

Using just these two properties we can easily proceed with the solution.

TIP -- Always consider everything a Geometrical figure has to offer. Never start a Geometrical question with a guess or an assumption.

Let me know if there is something else I can help you with in this question.

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