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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

#1
+142
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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.

Feb 23, 2019
edited by KeyLimePi  Mar 17, 2019
edited by KeyLimePi  Mar 17, 2019
#2
+104627
+3

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

EDIT TO CORRECT AN ERROR

Feb 23, 2019
edited by CPhill  Mar 17, 2019