# 2017 AMC 8 Problems/Problem 6

## Problem

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 1

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 $54:54:72$ $(3\cdot 18:3\cdot 18:4\cdot 18)$. The numbers in the ratio $54:54:72$ represent the angles of the triangle. The question asks for the largest, so the answer is $\boxed{\textbf{(D) }72}$.

## Solution 2

We can denote the angles of the triangle as $3x$, $3x$, $4x$. Due to the sum of the angles in a triangle, $3x+3x+4x=180^{\circ}\implies x=18^{\circ}$. The greatest angle is $4x$ and after substitution we get $\boxed{\textbf{(D) }72}$.

~MathFun1000

## Video Solution

~savannahsolver

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 