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Suppose that in a certain triangle, the degree measures of the exterior angles are in the ratio \(2:3:4\)

If the largest interior angle measures \(y^\circ\), what is the value of \(y\)?

 Feb 23, 2019

Given that the three angles are in the ratio, \(2:3:4\) we can write them as \(2a^\circ\)\(3a^\circ\), and \(4a^\circ\) for some number \(a\).

The sum of the interior angles of any triangle is \(180^\circ\), so we have
\(2a+3a+4a = 180\)
We can write this equation as  \(9a=180\)and solve to get \(a=20\). Thus the measures of the three angles are  \(2\cdot 20=40\) degrees,   \( 3\cdot 20=60\)degrees, and \(4\cdot 20=80\) degrees. In particular, if the largest angle is \(y^\circ\), then \(x=\boxed{80}\).


That's what I got and when I put it in it was correct. 


Edited: Ok I see what you did. You did the exterior angles but the problem asked for the interior angles. cool

 Feb 23, 2019
edited by KeyLimePi  Mar 17, 2019
edited by KeyLimePi  Mar 17, 2019

Let's look at this again


The exterior angles sum to 360


The smallest exterior angle will be supplemental to the largest  interior angle


So....the smallestt exterior angle is  (2/9)(360) = 80°


So...the largest interior angle = 180 - 80   =  100°  = y





cool cool cool

 Feb 23, 2019
edited by CPhill  Mar 17, 2019

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