The outer angle at the base of an isosceles triangle is 135 degrees prove that the triangle is right-angled

Since we know the external angle of the triangle, we can find the degree measure of the corresponding internal angle of the triangle:
180 – 135 = 45 °;
The triangle given to us is isosceles, which means that the angles that lie at the base in this triangle are equal.
This means that the second angle of the triangle will also be 45 °.
Now we can find the third corner and infer whether the given triangle is right-angled:
180 – 45 – 45 = 90 ° is the value of the third angle;
90 ° – right angle, respectively, the triangle will be rectangular.