Final answer:
The measure of angle COD is 147 degrees and the measure of angle POT is 137 degrees.
Step-by-step explanation:
Vertical angles are formed when two lines intersect and their sides are opposite rays. They are congruent, which means they have the same measure. In this case, the vertical angles are COP and TOD.
Given that m ZCOP = 11x - 17 and m TOD = 9x + 11, we can set these expressions equal to each other:
11x - 17 = 9x + 11
Subtract 9x from both sides and add 17 to both sides:
2x = 28
Divide both sides by 2:
x = 14
Now we can substitute the value of x back into the expressions for the angles:
m ZCOP = 11(14) - 17 = 147
m TOD = 9(14) + 11 = 137
Therefore, the measure of angle COD is 147 degrees and the measure of angle POT is 137 degrees.