Two complementary angles, A and B, have measures in the ratio of 7 to 23, respectively. What is the ratio of the measure of the complement of angle A to the measure of the complement of angle B? Express your answer as a common fraction.
7 + 23 = 30 sum of the ratios
90 / 30 = 3 constant ratio
[90 - (7 *3) ]=69 - complementary angle "A"
[90 - (23*3 ]=21 - complementary angle "B"
Ratio of A to B = 69 / 21 = 23 / 7
If two angles are complementary, then they add up to 90 degrees. Since the measures of angles A and B are in the ratio of 7 to 23, we can write A=7x and B=23x for some value of x. Substituting these values into the equation A+B=90, we get 7x+23x=90, which gives us x=2. Therefore, A=14 and B=46. The complements of angles A and B are 90−A=76 and 90−B=44, respectively. The ratio of the measures of the complements of angles A and B is 76/44=19/11.