The measures of the angle in the triangle are; ∠CDF = 43, ∠GDE = 63°, ∠FDG = 74°
From the way the problem is worded:
∠CDE is a straight angle made up of three angles:
∠CDF = 43°
∠FDG is unknown
∠GDE = 8x - 1
∠EDH is outside CDE = 6x + 15.
DE bisects GDH to form GDE and EDH.
Thus, we have;
8x - 1 = 6x + 15
x = 8
Putting 8 for x, both angles are equal to 57°.
Since ∠CDF = 43 and ∠GDE = 63° and ∠CDE ∠ 180° in total.
∠FDG = 180° - 43° - 63° = 74°
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