Question

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

Answer 1

The largest angle equals `48^o` and the smaller angle equals `42^o`.

Explanation:

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