The measures of two complementary angles are in a ratio 8:7. What is the measure of the smaller angle?

1 Answer
Nov 17, 2015

The largest angle equals 48^o48o and the smaller angle equals 42^o42o.

Explanation:

Let's assume that the two angles represent xx and yy. We know that x+y=90x+y=90. For this equation, let's assume yy is the bigger angle. yy would equal 8:7x, or to make it simpler, 8/7x87x. We can plug in 8/7x87x for yy in the original equation to get x+8/7x=90x+87x=90. Combining like terms, and then saying that x=7/7x=77, we get 15/7x=90157x=90. We then divide 15/7157 on both sides, and get x=42x=42. In the equation, y=8/7xy=87x, we add in 42 which makes y=48y=48. That's how we find out our answer.