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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

Sagot :

TSO
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.

[tex]\boxed{\sf{Answer~is~D~which~is~68,42,88}}[/tex]

View image TSO
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