There are 2 basic rules involved here. From them, a number of others can be derived in order to simplify some calculations.
angles forming a linear pair are supplementary (total 180°)
interior angles of a triangle total 180°
The derived relations we can use in this problem are ...
vertical angles are congruent
an exterior angle of a triangle is equal to the sum of the opposite interior angles
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<h3>c</h3>
The vertical angle to 78° is one of two remote interior angles with respect to exterior angle c. The other is the one marked 30°. That means ...
c = 78° +30* = 108°
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<h3>d</h3>
Angles d and 30° are two of the three angles in the largest triangle. The third is the vertical angle to 44°, so it is 44°. The sum of angles in that triangle is 180°:
You would rather flip the coin 500 times in the first game because over time the percentage should average out to that range.
You would flip the coin 25 times in the second game to let outliers have a greater chance of making a dramatic difference, like having the average be strayed from 50:50 to 25:75 or less
