Two supplementary angles have measures of 2(2x + 123) degrees and (x + 34) degrees. What is the measure of the smaller of the two angles?

Answer 1

Supplementary angles means the angles add up to a total of 180°.

Given one angle measures 2(2x+123) and the other angle measures (x+34), we can set up an equation.

2(2x+123)+(x+34)=180

Now we can solve for x.

2(2x+123)+(x+34)=180 (original equation)

4x+246+x+34=180 (distribute)

5x+280=180 (combine like terms)

5x=-100 (subtract 280 from both sides)

x=-20 (divide both sides by 5)

Now we can plug x back into the equations for the individual angles to find their measure.

Angle 1:

2(2x+123) (original expression)

2(2(-20)+123) (plug in x)

2(-40+123) (multiply)

2(83) (combine -40 and 123)

166 (multiply)

Angle 2:

(x+34) (original expression)

(-20+34) (plug in x)

14 (combine the numbers)

We know that 14<166 so Angle 2 is the smaller angle and measures 14°.

Hope this helps!