Question 1062915
<font color=black size=3>Let x and y be the two unknown angles.



They are supplementary, so they add to 180 degrees {{{x+y = 180}}}



Solve for y to get {{{y = 180-x}}} (subtract x from both sides)



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"one is 10 more than twice the other" means that 



{{{y = 2x+10}}}



Plug in {{{y = 180-x}}} and solve for x



{{{y = 2x+10}}}



{{{180-x = 2x+10}}} Notice how y is replaced with 180-x



{{{180-x+x = 2x+10+x}}}



{{{180 = 3x+10}}}



{{{180-10 = 3x+10-10}}}



{{{170 = 3x}}}



{{{3x = 170}}}



{{{3x/3 = 170/3}}}



{{{x = 170/3}}}



{{{x = 56.67}}} This is approximate



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Now plug {{{x = 170/3}}} into {{{y = 2x+10}}} to find y



{{{y = 2x+10}}}



{{{y = 2(170/3)+10}}}



{{{y = 340/3+10}}}



{{{y = 340/3+30/3}}}



{{{y = 370/3}}}



{{{y = 123.33}}} This is approximate


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We found that {{{x = 56.67}}} and {{{y = 123.33}}} approximately


So the two angle measures are approximately <font color=red>56.67 degrees and 123.33 degrees</font></font>