Question

I basically just have to find the angles but I also want to understand so if you could explain?

Answer 1

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.

1. angles forming a linear pair are supplementary (total 180°)
2. 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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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°

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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°