Answers:
x = 8
Angle GDH = 126 degrees
Angle FDH = 200 degrees
Angle FDE = 137 degrees
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Step-by-step explanation
Segment DE bisects GDH, so the angle pieces GDE and EDH are congruent.
We can write: angle GDE = angle EDH
That leads to the equation 8x-1 = 6x+15. It solves to x = 8. So you are correct. I'm not sure where your teacher is getting x = 7.
Use x = 8 to find the following angle measures:
- angle GDE = 8x-1 = 8*8-1 = 63
- angle EDH = 6x+15 = 6*8+15 = 63
- angle GDH = angle GDE + angle EDH = 63+63 = 126
You have the correct angle measure for angle GDH.
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Focus on the angles above the line CE. Those angles are:
- CDF = 43
- FDG = unknown, let's call it m
- GDE = 63
Adding up those angles should get us 180 degrees since the angles form a straight line.
CDF + FDG + GDE = 180
43 + m + 63 = 180
106+m = 180
m = 180-106
m = 74
Angle FDG is 74 degrees.
So,
angle FDH = angle FDG + angle GDH
angle FDH = 74 + 126
angle FDH = 200 degrees
And,
angle FDE = angle FDG + angle GDE
angle FDE = 74 + 63
angle FDE = 137 degrees