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Find ​(a) the complement and ​(b) the supplement of an angle with the measure 18 degrees 18 prime. Question content area bottom Part 1 ​(a) The complement of 18 degrees 18 prime is nothing degrees    nothing prime    . ​(Simplify your​ answer.)

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Answer to a math question Find ​(a) the complement and ​(b) the supplement of an angle with the measure 18 degrees 18 prime. Question content area bottom Part 1 ​(a) The complement of 18 degrees 18 prime is nothing degrees    nothing prime    . ​(Simplify your​ answer.)

Expert avatar
Rasheed
4.7
109 Answers
(a) To find the complement of an angle, we subtract the measure of the angle from 90 degrees.

Given that the measure of the angle is 18 degrees 18 prime, we first need to convert prime to minutes. Since there are 60 minutes in a degree, 18 prime is equal to 18 minutes.

Now we can calculate the complement:

Complement = 90 degrees - (18 degrees + 18 minutes)
= 90 degrees - (18 degrees + (18/60) degrees)
= 90 degrees - (18 degrees + 0.3 degrees)
= 90 degrees - 18.3 degrees
= 71.7 degrees

Therefore, the complement of an angle with the measure 18 degrees 18 prime is 71.7 degrees.

Answer: \boxed{71.7 \ \text{degrees}}

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(b) To find the supplement of an angle, we subtract the measure of the angle from 180 degrees.

Given that the measure of the angle is 18 degrees 18 prime, we first need to convert prime to minutes (as done in part (a)).

Now we can calculate the supplement:

Supplement = 180 degrees - (18 degrees + 18 minutes)
= 180 degrees - (18 degrees + (18/60) degrees)
= 180 degrees - (18 degrees + 0.3 degrees)
= 180 degrees - 18.3 degrees
= 161.7 degrees

Therefore, the supplement of an angle with the measure 18 degrees 18 prime is 161.7 degrees.

Answer: \boxed{161.7 \ \text{degrees}}

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