A pair of supplementary angles exists such that the larger of the two angles is 6 fewer degrees than twice the smaller angle.

Question

What is the degree measure of the larger angle?

Answer 1

The term supplementary means that both angels add up to 180 degrees. This gives us our first equation.

BigAngle + LittleAngle = 180 Degrees

 

The second equation we get from the question is:

 

BigAngle = (2 x LittleAngle) - 6 Degrees

 

Substitute the second equation into the first so that:

 

(2 x LittleAngle )- 6 Degrees + LittleAngle = 180 Degrees

 

Simplified this becomes:

 

3 x LittleAngle - 6 Degrees = 180 Degrees

 

Add 6 Degrees to each side.

 

3 x LittleAngle = 186 Degrees

 

Divide both sides by 3.

 

LittleAngle = 62 Degrees

 

Substitute 62 Degrees back into the first equation.

 

BigAngle + 62 Degrees = 180 Degrees

 

Subtract 62 Degrees from both sides

 

BigAngle = 118 Degrees