2017 AMC 8 Problems/Problem 6

Problem 6

If the degree measures of the angles of a triangle are in the ratio $3:3:4$ , what is the degree measure of the largest angle of the triangle?

$\textbf{(A) }18\qquad\textbf{(B) }36\qquad\textbf{(C) }60\qquad\textbf{(D) }72\qquad\textbf{(E) }90$

Solution

The sum of the ratios is $10$ . Since the sum of the angles of a triangle is $180^{\circ}$ , the ratio can be scaled up to $54:54:72$ . The numbers in the ratio $54:54:72$ represent the angles of the triangle. We want the largest, so the answer is $\boxed{\textbf{(D) }72}$

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2017 AMC 8 Problems/Problem 6

Problem 6

Solution