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 \(y\)?

KeyLimePi Feb 23, 2019

#1**+2 **

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.

KeyLimePi Feb 23, 2019