Question

The sum of the angles of a triangle is 180. Angle B and angle C are the same size. If angle A is 42 degrees smaller than angle B. Find the measure of each angle.

Answer 1

The sum of the angles of a triangle is 180. This means that

angle A + angle B + angle C = 180

If Angle B and angle C are the same size, it means that

angle B = angle C

If angle A is 42 degrees smaller than angle B, it means that

angle A = angle B - 42

We would substitute angle A = angle B - 42 into the first equation. It becomes

angle B - 42 + angle B + angle C = 180

We would substitute angle C = angle B in the equation above. It becomes

angle B - 42 + angle B + angle B = 180

angle B + angle B + angle B = 180 + 42 = 222

3 angle B = 222

angle B = 222/3

angle B = 74 degrees

angle C = angle B

angle C = 74 degrees

angle A = angle B - 42 = 74 - 42

angle A = 32 degrees