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

https://youtu.be/rQUwNC0gqdg?t=635

https://youtu.be/ykR1ApGP0Qg

~savannahsolver

See Also

2017 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AJHSME/AMC 8 Problems and Solutions

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