Answers:
- angle GFH = 60 degrees
- angle GHD = 110 degrees
- angle FGH = 10 degrees
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Explanation:
Angle CFG is given to be 120 degrees.
The angle to the right that's adjacent to this is angle GFH. The two angles add to 180
(angle CFG) + (angle GFH) = 180
(120) + (angle GFH) = 180
angle GFH = 180 - 120
angle GFH = 60 degrees
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Angle XGA is 70 degrees. Note how it corresponds to angle XHC since both angles are in the same northwest quadrant of their four-corner angle configuration.
Corresponding angles are congruent due to the parallel lines AB and CD.
This means angle XHC is also 70 degrees.
We'll use the same idea as in the last section
(angle XHC) + (angle GHD) = 180
(70) + (angle GHD) = 180
angle GHD = 180 - 70
angle GHD = 110 degrees
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Focus on triangle FGH.
We want to find angle FGH, which is the same as angle G when focusing solely on triangle FGH and no other points or triangles.
In the previous two sections, we found
- angle GFH = 60
- angle XHC = 110
This can be shortened to
- angle F = 60
- angle H = 110
Again we must focus solely on triangle FGH and nothing else.
So we have
- angle F = 60
- angle G = unknown
- angle H = 110
Let's solve for G
F+G+H = 180 .... angles of a triangle always add to 180
60+G+110 = 180
G+170 = 180
G = 180-170
G = 10
For triangle FGH, angle G is 10 degrees.
This means angle FGH is 10 degrees.
