In an isosceles triangle ABC with base AC, angle B is 42. Find the other two angles of triangle ABC.

An isosceles triangle is a triangle whose two sides are equal. One of the properties of an isosceles triangle says that the angles at the base are equal to each other. Thus, the angles A and C are equal, since they lie at the base of the triangle ABC.
The triangle sum theorem states that the sum of the angles of any triangle is 180 degrees. Then:
A + B + C = 180 degrees.
Since the angles A and C are equal, we denote them as x:
x + B + x = 180 degrees;
2x + 42 degrees = 180 degrees;
2x = 180 degrees – 42 degrees;
2x = 138 degrees;
x = 138 degrees / 2
x = 69 degrees.
Thus, angles A and C are equal to 69 degrees.
Answer: angle A = 69 degrees, angle C = 69 degrees.