An isosceles triangle with a base angle of 45 degrees is.

An isosceles triangle with a base angle of 45 degrees is right-angled. This can be proved using the triangle sum theorem, which states that the sum of all the angles of a given triangle is 180 °. Thus, if a triangle is isosceles and two of its angles are equal to 45 ° each, then the third angle of this triangle will be equal to 180 ° – 45 ° * 2 = 180 ° – 90 ° = 90 °, therefore, this angle is right, and the triangle – rectangular.