Triangle ABC has an exterior angle with measure 112 degrees. Which of the following could NOT be the measures of the angles of triangle ABC?
68,70,42
30,68,82
68,60,52
68,42,88
So open up the attachement I have posted so that way you can go along with me better. :)
So if the exterior angle is 112, then [tex]\sf{180-112 = z}[/tex]
So [tex]\sf{z=68}[/tex]
So that means any answer choice that does not have 68 has to be gone. Unfortunately, all of them have 48 so we can't eliminate any.
Also, [tex]\sf{x+y=112}[/tex] because x+y+z=180 but subtract the value of z which is 68 and we get that.
So that means that the other two angles in the answer choice should add upto 112.
A) 70+42 = 112 B) 30+82= 112 C) 60+52 = 112 D) 42+88 = 130
So D is the correct answer. Because it does not equal to 112
~After doing this I realized that there was an easier way~
Just add up all of the 3 angles in the answer choice to see if it equals to 180/ A) 68+70+42 = 180 B) 30+68+82 = 180 C) 68+60+52 = 180 D) 68+42+88 = 198
And 198 degrees in a triangle is not possible, so the answer is D.
