Math question about triangles

I'm having trouble on a homework problem and I really need help.

Question: The exterior angles of a triangle measure 5x, (x + 61), and (3x + 38). Which is the best classification of the triangle?

Options: acute, equiangular, obtuse, or right


I think the answer might be right, but I'm having trouble explaining why. Thank you!

The interior angles must be

180 - 5x
180 - (x + 61) = 119 - x
180 - (3x + 38) = 142 - 3x

(180 - 5x) + (119 - x) + (142 - 3x) = 180

261 = 9x
x = 29 degrees

180 - 5x = 35 degrees
119 - x = 90 degrees
142 - 3x = 55 degrees

So it's a right triangle.

Remember: All angles of a triangle add up to 180

5x+x+61+3x+38=180
9x+99=180
-99 -99
9x=81
_ _
9 9
x=9



Now plug x in to find the value of each angle

5(9)=45
(9)+61=70
3(9)+38=65

The angles are all acute so that means the triangle is an ACUTE TRIANGLE.

Hope that helped.