Angles P and Q are supplementary angle. If m∠P is three times m∠Q minus 4, what are the measures of the two angles?

Answer 1

Supplementary angles total 180 degrees

P + Q = 180

If P = 3Q - 4

Then

P + Q = 180

3Q - 4 + Q = 180

Combine like terms and solve for Q

While the information does not actually say the measure of P is three times the quantity Q -4, it could be easily interpreted as such.

P + Q = 180

3(Q - 4) + Q = 180

3Q - 12 + Q = 180

Again combine like terms and solve for Q.

Answer 2

Let the angle of Q be x, Angle P = 3x - 4

P + Q = 180 because they are supplementary,angles so 3x - 4 + x = 180.

Simplify, 4x - 4 = 180, 4x =184, x = 46 = angle Q

Therefore, angle P = 3(46) - 4 = 138 - 4 = 134. Answer: angle P = 134 degrees, angle Q = 46 degrees.