Question 157103
the three angles of a triangle are in a 1:2:3 ratio. What are their measurements?
<pre><font size = 4 color = "indigo"><b>
Let the angles be {{{A}}}, {{{B}}}, and {{{C}}}

{{{1}}} is to the sum {{{1+2+3}}} as {{{A}}} is to the sum {{{A+B+C}}}

{{{1/(1+2+3)=A/(A+B+C)}}}

But since {{{A+B+C=180}}}°

{{{1/(1+2+3)=A/180}}}

{{{1/6=A/180}}}

Cross-multiply:

{{{6A=180}}}

Divide both sides by 6

{{{A=30}}}°

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{{{2}}} is to the sum {{{1+2+3}}} as {{{B}}} is to the sum {{{A+B+C}}}

{{{2/(1+2+3)=B/(A+B+C)}}}

But since {{{A+B+C=180}}}°

{{{2/(1+2+3)=B/180}}}

{{{2/6=B/180}}}

Cross-multiply:

{{{6B=360}}}

Divide both sides by 6

{{{B=60}}}°

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To find the third angle you could just add those
two and subtract from 180°, but as a check you
could do it like the others:

{{{3}}} is to the sum {{{1+2+3}}} as {{{C}}} is to the sum {{{A+B+C}}}

{{{3/(1+2+3)=C/(A+B+C)}}}

But since {{{A+B+C=180}}}°

{{{3/(1+2+3)=C/180}}}

{{{3/6=C/180}}}

Cross-multiply:

{{{6C=540}}}

Divide both sides by 6

{{{C=90}}}°

Edwin</pre>