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

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

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Answer 1 · 2015-11-17T05:11:13

The largest angle equals $48^{o}$ $48^o$ and the smaller angle equals $42^{o}$ $42^o$ .

Explanation:

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

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

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