One corner of an isosceles triangle is 33 degrees less than the other. Find the corners of this triangle.

This problem can be solved in II ways.

Method I:

By the condition of the problem, the triangle is isosceles, that is, it has two equal angles. Let one angle be x degrees, then the other two are (x – 33) and (x – 33) degrees. According to the properties of the angles of a triangle, their sum is always 180 degrees. Let’s make the equation:

x + (x – 33) + (x – 33) = 180

x + x – 33 + x – 33 = 180

3x – 66 = 180

3x = 180 + 66

3x = 246

x = 246/3

x = 82

One of the angles is 82 degrees, then the other two angles are 82 – 33 = 49 degrees.

Answer: The angles of the triangle are 82 degrees, 49 degrees, 49 degrees.

II method:

By the condition of the problem, the triangle is isosceles, that is, it has two equal angles. Let the two angles be equal in x degrees, then the third angle is (x + 33) degrees. According to the properties of the angles of a triangle, their sum is always 180 degrees. Let’s make the equation:

x + x + (x + 33) = 180

x + x + x + 33 = 180

3x + 33 = 180

3x = 180 – 33

3x = 147

x = 147/3

x = 49

Two angles are 49 degrees, then the third angle is 49 + 33 = 82 degrees.

Answer: The angles of the triangle are 49 degrees, 49 degrees, 82 degrees,.