TheMastermind wrote:

Why can we not apply the exterior angle formula on angle CXY and angle XYB from the information in statement (1) to get the values for angle AXY and angle AYX?

Hi

TheMastermind ,

Even if you apply the exterior angle formula on statement 1, you will get

angle CXY = angle A + angle AYX -- (1)

angle XYB = angle A + angle AXY --(2)

Adding (1) and (2),

I will get,

angle CXY + angle XYB = 270

or 2 * angle A + angle AYX + angle AXY = 270

or angle AYX + angle AXY = 270 - 2 (90)

or angle AYX + angle AXY = 90.

Fine, we already know that the sum of these two angles is 90. So, we didn't find anything special.

Now, you cannot say that each of these angles are equal because we don't know whether we have AX = AY.

Hence, this method will not yield us what we want.

I hope that makes sense.

But the sum of those two angles is equal to 90. Shouldn't that mean that we have an isosceles right angles triangle with sides AX as equal to AY?