Question 1120157
The largest angle in a triangle is twice the degree measure of the second largest angle. one-third of the largest angle is 10 degrees larger than the difference of the other two. What is the measure in degrees of the smallest angle?
<pre>Let measures of smallest, middle, and largest angles be S, M, and L, respectively
Then L = 2M ------ eq (i)
Also, {{{matrix(1,7, (1/3) * L, "=", M - S + 10, "=====>", L/3, "=", M - S + 10 )}}} 
L = 3M - 3S + 30 --------- Multiplying by LCD, 3
2M = 3M - 3S + 30 -------- Replacing L with 2M
3S - 30 = M ------- eq (ii)
In addition, S + M + L = 180______S + M + 2M = 180______S + 3M = 180 ------ eq (iii)
S + 3(3S - 30) = 180 ------- Replacing M with 3S - 30 in eq (iii)
S + 9S - 90 = 180
10S = 270
S, or measure of smallest angle = {{{highlight_green(matrix(1,3, 270/10, "=", 27^o))}}}