∠F and ∠G are supplementary angles. If m∠F is two less than six times the measure of ∠G, find the measures of both angles.

Answer 1

Let F = the measure of angle F and G = measure of angle G. Since they are supplementary, then F + G = 180.

Also F equals 6 times G - 2 or F = 6G - 2. So now we have two equations:

F + G = 180

F = 6G - 2

We can plug in "6G - 2" wherever we see an F in the first equation so:

(6G - 2) + G = 180

7G - 2 = 180

7G = 182

G = 182/7 = 26 so the measure of angle G is 26°

Then, since F = 6G - 2, F = 6(26) - 2 = 154 so the measure of angle F is 154°