The ratio of an angle to its complement is 13:5. Find the measures of the angle and its supplement. ?

Question

5894 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-08T20:51:46

$65^{o}$ $65^o$ supplement is $115^{o}$ $115^o$
$25^{o}$ $25^o$ supplement is $155^{o}$ $155^o$

Since an angle and its complement add up to $90^{o}$ $90^o$ :

Ratio:

$13 : 5$ $13:5$

Add the ratio numbers and divide them into $90^{o}$ $90^o$

$\frac{90}{18} = 5$ $90/18=5$

So angles are:

$13 \times 5 = 65^{o}$ $13xx5=65^o$

$5 \times 5 = 25^{o}$ $5xx5=25^o$

An angle and its supplement add up to $180^{o}$ $180^o$

so:

$180^{o} - 65^{o} = 115^{o}$ $180^o-65^o=115^o$

$180^{o} - 25^{0} = 155^{o}$ $180^o-25^0=155^o$

I assume you are referring to the first angle, but have given you both so you can choose which is required.