SOLUTION: If two angels of a triangle are acute angles,then the third angle is? Less then the sum of the other two angles Is an acute angle Is an obtuse angle Is the largest angl

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Question 764136: If two angels of a triangle are acute angles,then the third angle is?
Less then the sum of the other two angles
Is an acute angle
Is an obtuse angle
Is the largest angle of the triangle
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

All of the choices are possible, but none of them is certain.

Proof: Let angle A and angle B be the given acute angles and angle C be the third angle.

and

By definition of acute

Since we can choose any value in that range for angles A and B, let's choose 89 degrees for each one.

Then the sum of the measures of the two angles is then 178 degrees. Since the sum of the three angles of any triangle is 180, Angle C must measure 2 degrees, which makes Angle C an acute angle.

So far we have validated the first two answers and invalidated the last two.

Now, let the measures of angle A and angle B each be 1 degree, making the measure of angle C 178 degrees.

This situation invalidates the first two answers but validates the last two.

Therefore the fact that two of the angles of a triangle are acute tells you nothing substantive except that you actually have a triangle. In fact EVERY triangle has at least two acute angles. I'll leave the proof of that assertion as an exercise for the student.

John

My calculator said it, I believe it, that settles it