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.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!