SOLUTION: Why does acute angles in an isosceles right triangle always measure 45 degrees?

Let's take a look at an isosceles right triangle:



We know that the measures of all three angles of any triangle
must have sum 180°.

We know that 90° of that 180° is in the measure of the right angle.
So that leaves 90° for the sum of the two acute angles. 

Since the triangle is isosceles, the two acute angles must
have the same measure.

So each one must have measure which is one-half of the remaining
90°.  And half of 90° is 45°.  So each of them must have measure 45°   

------------------------------

We could do it by angebra.  Suppose each of those acute angles has
measure x, since we know they have the same measure



Then adding the measures of the three angles:

             x + x + 90° = 180°

Combine the x terms:

                2x + 90° = 180°

Subtract 90° from both sides:

                     2x = 90°

Divide both sides by 2:

                      x = 45°

So we have:




Edwin