Final answer:
To find mZCDE, we first find mZCD and mZDE. Using the given values, we determine that mZCDE is 16°.
Step-by-step explanation:
To find the measure of angle ZCDE, we need to find the measure of angle ZCD and angle ZDE first.
Given that mZCDL = 98°, we can conclude that mZCD = 98° as angle L is adjacent to angle CD. Similarly, mZLDE = 65° as angle L is adjacent to angle DE.
Since angles CZD and EZD are supplementary angles (they add up to 180°), we can set up the equation: mZCD + mZDE = 180°.
Substituting the given values, we have 98° + mZDE = 180°. Solving for mZDE, we get mZDE = 180° - 98° = 82°.
Finally, to find mZCDE, we subtract the measure of angle ZDE from the measure of angle ZCD: mZCDE = mZCD - mZDE = 98° - 82° = 16°.
Therefore, the measure of angle ZCDE is 16°, which is not listed as one of the answer choices. None of the options provided (a) 17°, (b) 33°, (c) 65°, (d) 98°) matches the correct answer.