<PRE><B>Question 1044856</B>

One angle of a triangle has a measure of 66.  The measure of the third angle is 57 more than 1/2 the measure of the second angle.  The sum of the angle measures of a triangle is 180.  What is the measure of the second angle? What is the measure of the third angle?
&lt;pre&gt;&lt;b&gt;&lt;u&gt;1&lt;sup&gt;st&lt;/b&gt;&lt;/u&gt;&lt;/sup&gt; angle: 66
Let measure of &lt;b&gt;&lt;u&gt;2&lt;sup&gt;nd&lt;/b&gt;&lt;/u&gt;&lt;/sup&gt; angle be S
Then &lt;b&gt;&lt;u&gt;3&lt;sup&gt;rd&lt;/b&gt;&lt;/u&gt;&lt;/sup&gt; angle = {{{matrix(1,3, (1/2) * S + 57, or, S/2 + 57)}}}
Since the 3 angles sum to {{{180^o}}}, we get: {{{66 + S + S/2 + 57 = 180}}}
{{{S + S/2 + 123 = 180}}}_______{{{S + S/2 = 57}}}  
2S + S = 114 ------- Multiplying by LCD, 2
3S = 114
S, or measure of &lt;b&gt;&lt;u&gt;2&lt;sup&gt;nd&lt;/b&gt;&lt;/u&gt;&lt;/sup&gt; angle: {{{highlight_green(matrix(1,3, 114/3, or, 38^o))}}}
Measure of &lt;b&gt;&lt;u&gt;3&lt;sup&gt;rd&lt;/b&gt;&lt;/u&gt;&lt;/sup&gt; angle: {{{highlight_green(matrix(1,3, 38/2 + 57 = 19 + 57 = 76^o, or, 180 - (66 + 38) = 180 - 104 = 76^o)))}}}</PRE>