2017 AMC 8 Problems/Problem 6
Contents
Problem
If the degree measures of the angles of a triangle are in the ratio , what is the degree measure of the largest angle of the triangle?
Solution 1
The sum of the ratios is . Since the sum of the angles of a triangle is , the ratio can be scaled up to The numbers in the ratio represent the angles of the triangle. The question asks for the largest, so the answer is .
Solution 2
We can denote the angles of the triangle as , , . Due to the sum of the angles in a triangle, . The greatest angle is and after substitution we get .
~MathFun1000
Solution 3
We know the longest side must be denoted by the 4 in the ratio. Since the ratio is 3:3:4, we know that the longest side must be of the degree total (which for all triangles is 180). Thus,
~Ligonmathkid2
Solution 4 (Brute Force) NOT RECOMMENDED
Since we see the ratio is , we can rule out the answer of because the numbers in the ratio are too big to have . Also, we are trying to find the largest angle and all the other angles except for 72 are too small to be the largest angle. Using all this, our answer is .
~jason.ca
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
https://youtu.be/rQUwNC0gqdg?t=635
~savannahsolver
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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