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
__
<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°
__
<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°:
The answer to the question above is letter C. To explain the answer if the given question, a circle of 30 inches radius, if the central angle is 35 degrees, intersecting the circle forms an arc of length which is 18.33 inches.
