Find the measure of an angle, if six times of its complement is 12° less than twice of its supplement.

Let the required angle be x and it’s complement is y and it’s supplement is z.

⇒ x + y = 90

i.e. y = 90 – x

And, x + z = 180

i.e. z = 180 – x

Now, according to question,

Six times of complement of x is 12°

less than twice of its supplement.

i.e. 6y = 2z – 12

Putting the value of y and z in this equation,

⇒ 6 (90 – x) = 2 (180 – x) – 12

⇒ 540 – 6x = 360 – 2x – 12

⇒ 6x – 2x = 540 – 360 + 12

⇒ 4x = 192

⇒

⇒ x = 48°

Hence required angle is 48°.