Question 1113926

let’s two complementary angles be {{{alpha}}} and {{{beta}}} and let’s {{{alpha>beta}}}

if the ratio of two complementary angles is {{{17:13}}} we have

{{{alpha:beta=17:13}}}…eq.1
{{{alpha+beta=90}}}…eq.2

From eq.1 we have {{{13alpha=17beta}}} ->{{{alpha=17beta/13}}}
Substitute it in eq.2
{{{alpha+beta=90}}}…eq.2
{{{ 17beta/13 +beta=90}}}
{{{ 17beta +13beta=90*13}}}
{{{ 30beta=90*13}}}
{{{ beta=(90*13)/30}}}
{{{ beta=3*13}}}
{{{ beta=39}}}->is the measure of the smaller angle


Check:

Find {{{alpha}}} first
{{{alpha+39=90}}}
{{{alpha=90-39}}} 
{{{alpha=51}}}

{{{alpha:beta=17:13}}}…eq.1
{{{51:39=17:13}}}
{{{51*13=39*17}}}
{{{663=663}}}