document.write( "Question 1113926: The ratio of two complementary angles is 17:13.\r
\n" ); document.write( "\n" ); document.write( "What is the measure of the smaller angle? \n" ); document.write( "

Algebra.Com's Answer #728972 by MathLover1(20855) $\"\"$ $\"About$

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\n" ); document.write( "let’s two complementary angles be $\"alpha\"$ and $\"beta\"$ and let’s $\"alpha%3Ebeta\"$ \r
\n" ); document.write( "\n" ); document.write( "if the ratio of two complementary angles is $\"17%3A13\"$ we have\r
\n" ); document.write( "\n" ); document.write( " $\"alpha%3Abeta=17%3A13\"$ …eq.1
\n" ); document.write( " $\"alpha%2Bbeta=90\"$ …eq.2\r
\n" ); document.write( "\n" ); document.write( "From eq.1 we have $\"13alpha=17beta\"$ -> $\"alpha=17beta%2F13\"$
\n" ); document.write( "Substitute it in eq.2
\n" ); document.write( " $\"alpha%2Bbeta=90\"$ …eq.2
\n" ); document.write( " $\"+17beta%2F13+%2Bbeta=90\"$
\n" ); document.write( " $\"+17beta+%2B13beta=90%2A13\"$
\n" ); document.write( " $\"+30beta=90%2A13\"$
\n" ); document.write( " $\"+beta=%2890%2A13%29%2F30\"$
\n" ); document.write( " $\"+beta=3%2A13\"$
\n" ); document.write( " $\"+beta=39\"$ ->is the measure of the smaller angle\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check:\r
\n" ); document.write( "\n" ); document.write( "Find $\"alpha\"$ first
\n" ); document.write( " $\"alpha%2B39=90\"$
\n" ); document.write( " $\"alpha=90-39\"$
\n" ); document.write( " $\"alpha=51\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"alpha%3Abeta=17%3A13\"$ …eq.1
\n" ); document.write( " $\"51%3A39=17%3A13\"$
\n" ); document.write( " $\"51%2A13=39%2A17\"$
\n" ); document.write( " $\"663=663\"$
\n" ); document.write( " \n" ); document.write( "

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