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?

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

Video Solution

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

https://youtu.be/ykR1ApGP0Qg

~savannahsolver

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

2017 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AJHSME/AMC 8 Problems and Solutions

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

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2017 AMC 8 Problems/Problem 6

Contents

Problem

Video Solution

Solution 1

Solution 2

See Also