9514 1404 393
Answer:
c = 108°
d = 106°
Step-by-step explanation:
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
__
c
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°
__
d
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°:
d + 30° +44° = 180°
d = 180° -74° = 106°
