Answer: 60 degrees
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Reason:
Use the HL (hypotenuse leg) theorem to prove that triangle BCF is congruent to triangle DCF.
It then leads to the fact that angle BCF is congruent to angle DCF.
Set those angle expressions equal to one another. Solve for x.
angle BCF = angle DCF
4x+6 = 7x-12
4x-7x = -12-6
-3x = -18
x = -18/(-3)
x = 6
Then,
- angle BCF = 4x+6 = 4*6+6 = 30
- angle DCF = 7x-12 = 7*6-12 = 30
Both angles are the same measure to confirm the correct x value.
Lastly, add up those angles to get angle BCD.
30+30 = 60 degrees is the final answer.