Angle A and angle B are supplementary angles. Angle A is four less than three times angle B. Find the measures of the two angles.

Question

Angle A and angle B are supplementary angles. Angle A is four less than three times angle B. Find the measures of the two angles.

Answer 1

If A and B are supplementary angles, that means they sum to 180 degrees.

A + B = 180

If angle A if 4 less than 3B, then

A = 3B - 4

Now we have a linear system of equations that we can solve. I'll use substitution here, plugging 3B - 4 into the first equation for A.

(3B - 4) + B = 180

4B = 184

B = 46

Again using the fact that the angles must be supplementary,

A + B = 180

A + 46 = 180

A = 134.

The measures of angles A and B are 134 degrees and 46 degrees, respectively.