SOLUTION: An isosceles triangle has one 25 degree angle and the base angles are each (5x) classify the triangle by its angle measures

This problem does not tell us that the vertex angle is the
angle that is 25°.  Each of the base angles could be 25° as
well.

So there are two solutions:

Case 1: The vertex angle is the only one which is 25°,
and the base angles are 5x each:



In this case the sum of all three angle measures must equal 180°,

so we have the equation:

25° + 5x + 5x = 180°

    25° + 10x = 180°

          10x = 180° - 25°

          10x = 155°

            x = 15.5° 

So since each of the base angles have measure 5x in this
case, each base angle is 5(15.5°) or 77.5°, so the
three angles are 25°, 77.5° and 77.5°.
This angles is an acute isosceles triangle because
it has three acute angles, which means they are all
less than 90°.

But we also have

Case 2: The base angles have measure 5x each:



In this case the vertex angle = 180° - 25° - 25° = 180° - 50° = 130°

The angles are 25°, 25°, 130°

So since one of the angles has measure 130° in this
case, this triangle is an obtuse isosceles triangle because
it has one obtuse angle, which means its measure is 
greater than 90°.

Notice that a triangle only needs ONE obtuse angles to be
classified as an obtuse triangle, but it requires THREE
acute angles to be classified as an acute triangle.  The
reason is that EVERY triangle has at least two acute
angles anyway!

5x = 25°
 x = 5°
     
We didn't have to find x for this case, but as we see it is 5°,
in case you had been asked for x.

Edwin