To find the measure of the unknown angle, we first recognize that we can use the information provided about the angles at intersection point G.
- We know the measure of angle F-G-E is 22 degrees.
- We also know the measure of angle A-G-B is 60 degrees.
At point G, the angles created by the intersecting lines will sum up to 360 degrees.
The angles that surround point G can be categorized as:
- F-G-E = 22 degrees
- A-G-B = 60 degrees
- The angles opposite to these angles can be calculated as they are vertically opposite angles or linear pairs.
Since angle F-G-E and the angle that is next to it (let's call it angle E-G-A) form a linear pair, we can calculate angle E-G-A as: \[ \text{Angle E-G-A} = 180° - \text{Angle F-G-E} = 180° - 22° = 158° \]
Next, angle A-G-B and the angle next to it (let's call it angle B-G-C) form another linear pair: \[ \text{Angle B-G-C} = 180° - \text{Angle A-G-B} = 180° - 60° = 120° \]
Now we have the following angles at point G:
- Angle F-G-E = 22°
- Angle A-G-B = 60°
- Angle E-G-A = 158°
- Angle B-G-C = 120°
To find the measure of the unknown angle, we should identify which angle is missing. Since all angles around point G must add up to 360 degrees, we calculate: \[ 22° + 60° + 158° + 120° = 360° \]
However, the values above give us the angles around point G, meaning that the unknown angle will be the one opposite to F-G-E or A-G-B:
Let's denote the angles at G as follows:
- \( \angle F-G-E = 22° \)
- \( \angle E-G-A = 158° \)
- \( \angle A-G-B = 60° \)
- \( \angle B-G-C = 120° \)
Opposite angle to F-G-E is A-G-B. Thus, we don’t need to reassess all angles.
From this, we calculate: \[ x + 22° + 60° = 180° \] Where x is the angle opposite ar (we don't need x, we just know )
Now let's look at C-G-F (the angle opposite to A-G-B): is equal to angle F-G-E.
This also means that we are looking at x (angle C-G-F).
Concentrating on that, we need to find the new \(x (C-F-A)\) which would be opposite.
160+ x + 120 + y= 360
This indicates that we are looking for:
Subtracting: x must be 180- 22 = 158 +120 = 360
Thus finding opposite angle of x means that sum of angles which could suggest that \(y = 360 - x - y\)
Focusing on opposing pairs.
By reasoning above using the inscribed angles theorem implies that:
Final measures suggest properly that it might extend to find \(x\), but as we know;
Therefore:
The angle we are looking for could very well suggest what remains as calculations fall in line provides which can provide the answer as found through simplistically:
Therefore: The measure of the unknown angle could be interpolated of being 90 degrees as intended based on pairs suggesting error validated down to line segments arrangements.
So the correct response is \(C: 90°\) which aligns to simplifying conditionally by the angles presented if isolating findings.
Thus the unknown angle \(90° = 90\) will provide statement see by calculated inference.
Therefore the answer is C. 90°.
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