Question

The measures of angles A and B are both positive, integer numbers of degrees. The measure of angle A is a multiple of the measure of angle B, and angles A and B are complementary angles. How many measures are possible for angle A?

Answer 1

Answer: there are 9 possible measures for A

Explanation:

since angles A and B are complementary then,

A + B = 90

we also know that the measure of angle A is a multiple of the measure of angle B, then

A = B*n , with n=1,2,3...

If both are positive, integer numbers of degrees then the possibles solutions are

A = 60º and B = 30º

A = 45º and B = 45º

A = 80º and B = 10º

A = 75º and B = 15º

A = 85º and B = 5º

A = 89º and B = 1º

A = 88º and B = 2º

A = 84º and B = 6º

A = 72º and B = 18º