Find the angles of an isosceles triangle if one is 27 degrees larger than the other.

In an isosceles triangle, the angles at the base are equal. And in an isosceles triangle, the angles at the base can only be sharp, so if there is a larger and smaller angle, then the smaller one is considered at the base. If one of the angles is 27 degrees larger than the other, then the other two are the same in relation to each other, so they are at the base. We take this larger angle as x + 27, then the other as x and three times at the base also as x. Sum of angles:
x + (x + 27) + x = 180, hence 3x = 180-27, hence 3x = 153, x = 51. So the angles are 51 degrees, 78 degrees, 51 degrees.