ABC, angle B = 32, and outer angle C = 64, Find angle A.

The problem can be solved in different ways, using the properties of the outer corners of the triangle.

1.
The sum of the outer and inner angles at one vertex is 180 °. Find the angle C (internal) = 180 ° – 64 ° = 116 °.
The angles of a triangle add up to 180 °. Find corner A.
angle A = 180 ° – (116 ° + 32 °) = 180 ° – 148 ° = 32 °.

2.
The outer angle of a triangle is equal to the sum of the other two angles of the triangle that are not adjacent to it. Using this property, we immediately find the angle A of the triangle:
angle A = angle C (outer) – angle B (triangle) = 64 ° – 32 ° = 32 °.
Answer: the angle A of the triangle is 32 °.