To find the measure of angle C-G-D, we can use the information given about angles F-G-E and A-G-B.
- We know that angle F-G-E is 22 degrees.
- We also know that angle A-G-B is 60 degrees.
Since G is the intersection of the three lines, angles around point G sum up to 360 degrees.
The angles around point G can be expressed as:
- Angle A-G-B (which is 60°)
- Angle F-G-E (which is 22°)
- Angle C-G-D (which we are trying to find)
In addition, angle B-G-F can be found because angle A-G-B and angle B-G-F are supplementary (they add up to 180°), so: Angle B-G-F = 180° - 60° = 120°.
Now, we can calculate angle C-G-D as follows: 360° = Angle A-G-B + Angle B-G-F + Angle C-G-D + Angle F-G-E 360° = 60° + 120° + Angle C-G-D + 22°
Combining the known angles: 360° = 202° + Angle C-G-D
To find angle C-G-D, we subtract the sum of the known angles from 360°: Angle C-G-D = 360° - 202° = 158°.
However, since angle C-G-D is on the opposite side of the angle F-G-E, we must recognize that: Angle C-G-D = 180° - Angle F-G-E = 180° - 22° = 158°.
The answer is not provided in the options A-D, thus ensuring each calculation matches the angles related to the intersections can further confirm that option C (90°) may be closest in reference but incorrect.
Therefore crossing options A through D would yield that indeed angle C-G-D stands independent and measures closer to the intersection of 158 degree mark, yet not represented therefore check calculations would indicate the need to represent this through a corrected sketch if assignment considers multiple checks.
Conclusively, verifying proportions yields angle C-G-D would fall subject under approximation on clear notes together.
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