2017 AMC 8

Complete problem set with solutions and individual problem pages

Problem 6 Easy

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?

  • A.

    18

  • B.

    36

  • C.

    60

  • D.

    72

  • E.

    90

Answer:D

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}.

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