Question

One-half of the supplement of an angle is twelve less than twice the complement of the angle. Find the angle.

Answer 1

x = 52

let x be the angle then $\frac{1}{2}$ (180 - x ) represents one half of the supplement of the angle and

2( 90 - x ) - 12 represents 12 less than twice the complement of the angle

equating these 2 expressions

$\frac{1}{2}$ (180 - x ) = 2(90 - x ) -12

distribute brackets on both sides

90 - $\frac{1}{2}$ x = 180 - 2x - 12 = 168 - 2x

add 2x to both sides

90 + $\frac{3}{2}$ x = 168 → ( subtract 90 from both sides )

$\frac{3}{2}$ x = 78

multiply both sides by 2 and divide by 3

x = 52

Answer 2

The value of angle is 52 degree.

What are Complementary and Supplementary Angles ?

When sum of two angles is equal to 90 degree then they are called complementary angle and when the sum is equal to 180 degree then the two angles are called supplementary angle.

It is given in the question

One-half of the supplement of an angle is twelve less than twice the complement of the angle

Let the angle be x

Supplement of the angle will be 180- x

Complement of the angle will be 90-x.

Now from the question

(1/2) * 180- x  = 2 * (90-x) - 12

180- x = 4 * (90-x) -24

180- x = 360 - 4x -24

3x = 360-24-180

3x = 156

x  =52 degree

Therefore the value of angle is 52 degree.

To know more about Complementary and Supplementary Angles

https://brainly.com/question/3027144

#SPJ2