Geometric Problem figure

[Brainiachotd]

I've been trying to find the right answer for this one since i was doubting what the correction key was saying for this sample prob. I believed that variable a and 142 are interior angles which lead up to 180 degrees while b can be obtained thru minusing it with 142 since b make up an interior angle as well. However im not sure if the correct answer is 84 since the correction key says its 218.
Note: i checked the correction key and some of it has errors

 

[Dr.Peterson]

All three angles are exterior angles. None are on the inside of the triangle.

What is the sum of the three exterior angles of a triangle? One way to see it is to imagine sliding one of the lines until they all intersect at one point; then you can see why these three angles add up to that sum. (It will be easier to see if you move the label "a" to its vertical angle.)

The key's answer is correct.

 

[LCKurtz]

I can see why the OP might be unsure about it since the figure shows [MATH]142^\circ[/MATH] as an acute angle. Maybe he thought that was a typo (grapho?).

 

[Brainiachotd]

Thanks guys for answering my test question. That atleast cleared my doubts