Final answer:
To find the measure of angle ZQ, we use the fact that angles ZP and ZQ are supplementary. Subtracting the measure of angle ZP from 180 degrees gives us the measure of angle ZQ. mZQ = 123 degrees.
Step-by-step explanation:
To solve for mZQ, we need to use the fact that ZP and ZQ are supplementary angles.
Supplementary angles add up to 180 degrees. So, we have the equation mZP + mZQ = 180.
Substituting the given values mZP = 4x + 1 and mZQ = 9x - 3, we get 4x + 1 + 9x - 3 = 180.
Simplifying this equation gives us 13x - 2 = 180. Solving for x gives us x = 14.
Finally, substituting x = 14 into mZQ = 9x - 3 gives us mZQ = 9(14) - 3 = 123 degrees.