Answer: 42°
Step-by-step explanation: In this problem, we're given that the measures of two complementary angles are in the ratio 7 to 8 and we're asked to find the measure of the smaller angle.
Since our two angles are in the ratio 7 to 8, let's represent the angles as 7x and 8x. We will call 7x an angle and 8x its complement. Now, remember that if two angles are complementary, then the sum of their measures is 90 degrees. So we can set up the equation 7x + 8x = 90.
Simplifying on the left side, we have 15x = 90.
Dividing both sides by 15, we find that x = 6.
So the measure of our first angle, 7x, is 7(6) or 42°.
The measure of its complement, 8x, is 8(6) or 48°.
Finally, notice that if we add our two angles together, we have 42 + 48 which equals 90 so our answer checks. This means that the smaller angle is 42°. Image is provided below.
