Question 921583

given:
Two angles are supplementary.

{{{alpha+beta=180}}}.........eq.1

One angle is {{{15}}} degrees less than {{{2}}} times the other angle:

{{{alpha+15=2beta}}}..........eq.2

solve the system:

{{{alpha+beta=180}}}.........eq.1
{{{alpha+15=2beta}}}..........eq.2
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{{{alpha+beta=180}}}.........eq.1...solve for {{{alpha}}}

{{{alpha=180-beta}}}........substitute in eq.2


{{{180-beta+15=2beta}}}..........eq.2..........solve for {{{beta}}}


{{{180+15=2beta+beta}}}

{{{195=3beta}}}

{{{65=beta}}}


now find {{{alpha}}}

{{{alpha=180-beta}}}

{{{alpha=180-65}}}

{{{alpha=115}}}