4. Alex draws a scalene triangle. One of the angles is $80^{\circ}$.
Which of the following could be the difference between the other two angles in Alex's triangle?
A $0^{\circ}$
B $60^{\circ}$
C $80^{\circ}$
D $100^{\circ}$
E $120^{\circ}$
Solution
C

All the side lengths of a scalene triangle are different, therefore all the angles are different.
It follows that the difference between two of the angles cannot be $0^{\circ}$. This rules out option A.
The sum of the angles in a triangle is $180^{\circ}$. Therefore, as one of the angles in Alex's triangle is $80^{\circ}$, the sum of the other two angles is $100^{\circ}$. It follows that the difference between these angles is less than $100^{\circ}$. This rules out options D and E.
If the two angles with sum $100^{\circ}$ have a difference of $60^{\circ}$, these angles would be $80^{\circ}$ and $20^{\circ}$. So the triangle would have two angles of $80^{\circ}$, which is impossible for a scalene triangle. This rules out option B.
Therefore the correct option is $\mathrm{C}$, since it is the only one we have not eliminated.