document.write( "Question 243712: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is \n" ); document.write( "

Algebra.Com's Answer #178517 by oberobic(2304) $\"\"$ $\"About$

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This problem hinges on your remembering that the sum of the angles in a triangle is always 180.
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\n" ); document.write( "In this case we have 3 unknown angles: a, b, and c.
\n" ); document.write( "However, we are told they have a specific relationship: 1 to 3 to 5. So the second angle is 3 times the first and the third angle is 5 times the first.
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\n" ); document.write( "a = a
\n" ); document.write( "b = 3a
\n" ); document.write( "c = 5a
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\n" ); document.write( "a + b + c = 180
\n" ); document.write( "Substituting,
\n" ); document.write( "a + 3a + 5a = 180
\n" ); document.write( "9a = 180
\n" ); document.write( "Divide both sides by 9
\n" ); document.write( "a = 20
\n" ); document.write( ".
\n" ); document.write( "Substituting back into the formulas we defined.
\n" ); document.write( "a = 20
\n" ); document.write( "b = 3a = 3(20) = 60
\n" ); document.write( "c = 5a = 5(20) = 100
\n" ); document.write( ".
\n" ); document.write( "Check the work.
\n" ); document.write( "Does 20 + 60 + 100 = 180?
\n" ); document.write( "Yes.
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\n" ); document.write( "Done. \n" ); document.write( "

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