Question

An angle measures 126° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

27° and 153°

Explanation:

Let "x" represent the angle.

We know that supplementary angles must add up to 180 degrees.

First, let's set up an expression for the supplement of the angle "x":

x+126

Now, let's use this information to set up an equation:

`x+x+126=180`

Combine like terms:

`2x+126=180`

Subtract 126 from both sides:

`2x=54`

Divide both sides by 2

`x=27`

The supplement would be:

`x+126=27+126=153`

Therefore the measures of the two angles are:

27° and 153°

Answer 2

We know that:

• A pair of supplementary angles always sum up to 180°

This means that:

• 
  `x + x + 126 = 180`

Step-by step calculations:

Combine like terms and simplify:

• 
  `x + x + 126 = 180`
• =>
  `(x + x) + 126 = 180`
• =>
  `2x + 126 = 180`

Subtract 126 both sides:

• =>
  `2x + 126 - 126 = 180 - 126`
• =>
  `2x = 54`

Divide 2 both sides:

• =>
  `(2x)/(2) = (54)/(2)`
• =>
  `x = 27`

This means that one angle is 27°. Let's find the other angle.

Finding the other angle:

• 
  `27 + 126 = Other \space\ angle`
• =>
  `153 \space\ = Other \space\ angle`

Thus, the measure of the angles are 27° and 153°.