Find the angle A of a right-angled triangle ABC (angle C = 90 °) if angle B is 30 °, 70 °.

We know from the condition that a right-angled triangle ABC is given, and the angle C = 90 °. And it is also known that the angle B is equal to 1) 30 °; 2) 70 °.

In both cases, we need to find the degree measure of the third angle of triangle A.

To solve the problem, we apply the theorem on the sum of the angles of a triangle. The theorem says that the sum of the angles of a triangle is 180 °.

That is:

angle A + angle B + angle C = 180 °.

Let us express the angle A:

angle A = 180 ° – (angle B + angle C).

1) angle B = 30 °;

angle A = 180 ° – (30 ° + 90 °) = 180 ° – 120 ° = 60 °;

2) angle D = 70 °;

angle A = 180 ° – (70 ° + 90 °) = 180 ° – 160 ° = 20 °.