Question

Two angles whose sum is 180 degrees are supplementary angles.The larger angle measures 108 degrees The smaller angle measures ___ degrees

Answer 1

- The smaller angle is (6x + 6) while the larger angle is (9x + 9) by observation.

- Thus, we can find the value of x since we also know that the larger angle is 108 degrees.

- After finding x, we can find the measure of the smaller angle.

- Thus, we have:

`\begin{gathered} 9x+9=108 \\ \text{ Divide both sides by 9} \\ (1)/(9)(9x+9)=(108)/(9) \\ \\ x+1=12 \\ x=12-1 \\ x=11 \\ \\ \text{ Now that we know that }x=11,\text{ we can find the value of the smaller angle as } \\ \text{ follows:} \\ 6x+6=6(11)+6=72 \end{gathered}`

Final Answer

The measure of the smaller angle is 72 degrees