What are the measures of angles a, b, and c? show your work and explain your answers.
Asked by maham237 @ in Mathematics viewed by 305 People
What are the measures of Angles a, b, and c? Show your work and explain your answers.
Answered by maham237 @
Answer:
(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°.
___
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°
___
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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