$∠ X$ $/_X$ and $∠ Y$ $/_Y$ are supplementary. One angle measures 5 times the other angle. What is the complement of the smaller angle?

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Answer 1 · 2018-01-27T11:09:11

The complement of the smaller angle measures 60°.

The measures of supplementary angles add up to 180°. So if the angles measure $θ$ $\theta$ and $5 θ$ $5\theta$ , then

$\theta+5\theta=180°$

$6\theta=180°$

$\theta=30°$

Now we need the complement of this angle. The measures of complementary angles add up to 90°, so:

$90°-\theta=60°$

Answer 2 · 2018-01-27T11:17:52

The smaller angle is $30°$ and its complement is $60°$

Let the smaller angle, $hatX,$ be $x°$ , then the larger angle $hatY$ is $5x°$

Supplementary angles add up to $180°$

$x° +5x° = 180°$

$6x° = 180°$

$x = (180°)/6 =30°$

So the smaller angle, $hatX = 30°$

Complementary angles add up to $90°$

So the complement of the smaller angle is $90°-30° = 60°$

/_X∠X/_X and /_Y∠Y/_Y are supplementary. One angle measures 5 times the other angle. What is the complement of the smaller angle?