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Measure of largest angle in triangle

Source: AMC 10 2011 b Problem 7

February 24, 2011
AMCanglesgeometry

Problem Statement

The sum of two angles of a triangle is 65\frac{6}{5} of a right angle, and one of these two angles is 30∘30 ^\circ larger than the other. What is the degree measure of the largest angle in the triangle?
<spanclass=′latex−bold′>(A)</span> 69<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 90<spanclass=′latex−bold′>(D)</span> 102<spanclass=′latex−bold′>(E)</span> 108 <span class='latex-bold'>(A)</span>\ 69 \qquad <span class='latex-bold'>(B)</span>\ 72 \qquad <span class='latex-bold'>(C)</span>\ 90 \qquad <span class='latex-bold'>(D)</span>\ 102 \qquad <span class='latex-bold'>(E)</span>\ 108
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