Final answer:
Given value, x is 8. Using this value, we can find that angle GDE and EDH are both 63 degrees. Subtraction of the given angle CDF from 180 degrees (a straight angle's measure) gives us the measurement of the angle CDE as 137 degrees.
Step-by-step explanation:
This question falls under the category of Geometry, more specifically, angle and line properties. Since it's given that angle CDE is a straight angle, we can deduce that it measures 180 degrees. Also, it's mentioned that DE bisects angle GDH. This means that angle GDE equals angle EDH.
Therefore, we can set the equations of these two angles equal to each other: 8x - 1 = 6x + 15. If you solve this equation, you find that x equals 8. Applying this value of x to angle GDE and EDH, we find that angle GDE = 63 degrees and angle EDH = 63 degrees as well. Now, if we look at angle CDF, which according to the question is 43 degrees, it appears to be part of the larger angle CDE. So to find the angle CDE, we can subtract the angle CDF from the total of a straight angle. Thus, angle CDE = 180 - 43 = 137 degrees.
Learn more about Finding Angles