What are the measures of angles a, b, and c? show your work and explain your answers.

  (a, b, c) = (30°, 60°, 105°)

Step-by-step explanation:

Angle "a" and 30° are vertical angles, hence equal.

Angle "b" and angle "a" are complementary angles, so b = 90° -30° = 60°.

Angle "c" is supplementary to the one marked 75°, so is 180° -75° = 105°.

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Angles "a" and "b" are complementary because the sum of angles in a triangle is 180° and the third angle in that triangle is 90°. Then ...

  a+b = 180°-90° = 90°

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75° and "c" are supplementary, because they are linear angles. The angle measure of a line is 180°, so that is their total measure.

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step-by-step explanation: