Question

Find the measures of the complementary angles that satisfy each case. The measure of the first angle is 45 more.

a) 45° and 45°
b) 22.5° and 67.5°
c) 30° and 60°
d) 60° and 30°

Answer 1

To find the measures of complementary angles where one angle is 45 degrees more than the other, set up the equation x + (x - 45) = 90 and solve for x, finding the two angles to be 67.5 degrees and 22.5 degrees respectively.

Step-by-step explanation:

The student asked for the measures of complementary angles where the measure of the first angle is 45 degrees more than the second angle. By definition, complementary angles add up to 90 degrees. Therefore, if we call the measure of the first angle x and the second angle x - 45, we can set up the equation x + (x - 45) = 90. Solving this equation, we get 2x - 45 = 90, which leads to 2x = 135, and therefore x = 67.5 degrees. That means the measures of the two angles are 67.5 degrees and 22.5 degrees respectively.