Question

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

Answer 1

Solution:

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:

• => $\frac{2x}{2} = \frac{54}{2}$
• => $x = 27$

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°.

Answer 2

Answer:

27° and 153°

Step-by-step 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°