[[1]] is the measure of an angle which is five times its complement and is $12 °$ less than twice its supplement.

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answer is 34 °.

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Detailed Solution

34 °

is the measure of an angle which is five times its complement and is

12 °

less than twice its supplement.
We know,
An angle is five times its complement and is

12 °

less than twice its supplement.
Supplementary angles are those who sum up to

180 °

.
Complementary angles are those who sum up to

90 °

.
Let the measure of the angle be x.
The supplement of x will be

180 ° − x

.
The complement of it will be

90 ° − x .

Using the data given to form an equation,

5 (90 ° − x) = 2 (180 ° − x) − 12 ° 450 ° − 5 x = 360 ° − 2 x − 12 ° 3 x = 102 x = 34 °

Therefore, the measure of an angle whose 5 times complement is

12 °

less than twice its supplement is

34 °

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