Question 10910
We have three angles: one angle is two degrees larger than another.  Let's define the smaller of these two angles as {{{x}}}.  Thus, we can define the larger angle in terms of {{{x}}}, as {{{x+2}}}.

We can also define the third angle in terms of the other two!  The problem tells us that the sum of the first two angles, e.g., {{{x+x+2}}}, is 28 degrees larger than the third.  Rewording this, we know that the third angle is 28 degrees *smaller* than the sum of the other two.  Thus, the measure of the third angle is equal to {{{(x+x+2) - 28}}} = {{{2*x - 26}}}.

So now we have three expressions for the angles of this triangle: {{{x}}}, {{{x+2}}}, and {{{2*x-26}}}.  But how do we solve for {{{x}}}?


Remember, in any triangle, the sum of the measures of the angles is always 180 degrees.  Thus: {{{(x) + (x+2) + (2*x-26) = 180}}}.

Simplifying this yields:
{{{(x+x+x)+(2-26) = 180}}}
{{{4x - 24 = 180}}}
{{{4x = 204}}}
{{{x = 51}}}


Now, we substitute x into the expressions we calculated earlier.  Thus, the measure of the first angle is equal to {{{x = 51}}} degrees, the second is {{{(x+2) = (51+2) = 53}}} degrees, and the third is {{{2*x-26 = 2*(51)-26 = 76}}} degrees.


Thus, our triangle's angles are 51, 53, and 76 degrees.  To verify that this solution is correct, we just need to add them up.  Sure enough, {{{51+53+76 = 180}}}, which we know should be the sum of the angles of a triangle.