9514 1404 393
Answer:
a = 102°
b = 78°
c = f = 58°
d = 122°
e = 26°
Step-by-step explanation:
The usual rules apply:
- the sum of angles in a triangle is 180°
- the sum of angles making a right angle is 90°
- vertical angles are congruent
- corresponding angles at a transversal crossing parallel lines are congruent
- angles of a linear pair are supplementary.
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There are a couple of angles we can find right away:
b corresponds to 78°, so has that measure
a is supplementary to b, so is 180° -78° = 102°
e is complementary to 64°, so is 26°
The unmarked angle between 78° and f is vertical to 44°, so we have ...
78° +44° +f = 180°
f = 58°
Angle c corresponds to angle f, so is 58°
Angle d is supplementary to angle c, so is 180° -58° = 122°
In summary, ...
a = 102°
b = 78°
c = f = 58°
d = 122°
e = 26°
