Question 988110



first angle of a triangle is {{{alpha=highlight(66 )}}}degrees

the second angle is {{{beta}}}

the third angle{{{gamma}}}  is {{{57}}} degrees more than {{{1/2}}} the measure of the second angle  {{{beta}}}: so the third angle is  {{{gamma=(1/2)beta+57}}}

the sum of all is {{{180}}} degrees:

{{{alpha+beta+gamma=180}}}....substitute {{{66}}} for {{{alpha}}} and {{{(1/2)beta+57}}} for {{{gamma}}}

{{{66+beta+(1/2)beta+57=180}}}......solve for {{{beta}}}

{{{2beta/2+(1/2)beta+123=180}}}

{{{(3/2)beta=180-123}}}

{{{(3/2)beta=57}}}

{{{3beta=57*2}}}

{{{3beta=114}}}

{{{beta=114/3}}}

{{{beta=38}}}->the second angle

the third angle will be {{{gamma=(1/2)beta+57}}}=>{{{gamma=(1/2)*38+57}}}=>{{{gamma=19+57}}}=>{{{gamma=76}}}



so, 
the measure of the second angle is {{{highlight(38)}}} degrees

the measure of the third angle is {{{highlight(76)}}} degrees