Difference between revisions of "2017 AMC 8 Problems/Problem 6"
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==Solution 2== | ==Solution 2== | ||
We can denote the angles of the triangle as <math>3x</math>, <math>3x</math>, <math>4x</math>. Due to the sum of the angles in a triangle, <math>3x+3x+4x=180^{\circ}\implies x=18^{\circ}</math>. <math>4x</math> is the greatest angle and after substitution we get <math>\boxed{\textbf{(D) }72}</math>. | We can denote the angles of the triangle as <math>3x</math>, <math>3x</math>, <math>4x</math>. Due to the sum of the angles in a triangle, <math>3x+3x+4x=180^{\circ}\implies x=18^{\circ}</math>. <math>4x</math> is the greatest angle and after substitution we get <math>\boxed{\textbf{(D) }72}</math>. | ||
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| + | ~MathFun1000 | ||
==See Also== | ==See Also== | ||
Revision as of 09:29, 6 January 2022
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?
Video Solution
https://youtu.be/rQUwNC0gqdg?t=635
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, 
. is the greatest angle and after substitution we get .
~MathFun1000
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
