Final answer:
To find the value of z that makes lines p and q parallel with angles given as 9x and 117 degrees, solve the equation 9x = 117 to get x = 13. Thus, when x is 13, p and q are parallel.
Step-by-step explanation:
To find the value of z for which lines p is parallel to line q, given that m<1 = (9x) and m<3 = 117, we need to use the properties of parallel lines and the angles they create. When two lines are parallel, the corresponding angles are equal. This means that if angle 1 and angle 3 are corresponding angles, then m<1 = m<3 when lines p and q are parallel.
Given m<1 is 9x degrees and m<3 is 117 degrees, we can set them equal to each other because p and q are parallel:
9x = 117
To solve for x, we divide both sides of the equation by 9:
x = 117 / 9
x = 13
Therefore, when x equals 13, lines p and q are parallel.