Answer:
m∠FCD = 57°
Explanation:
Let m∠BCG = x°.
If m∠GCF is 9° less than m∠BCG, then m∠GCF = (x - 9)°.
When a ray bisects an angle, it divides it into two congruent angles.
Since CH bisects ∠GCD then m∠GCF = m∠FCD.
Therefore, m∠FCD = (x - 9)°.
As CA and CE are opposite rays, BC is a straight line.
Since angles on a straight line sum to 180°, then:
m∠BCG + m∠GCF + m∠FCD = 180°
Substitute the expressions for each angle into the equation:
x° + (x - 9)° + (x - 9)° = 180°
Solve the equation for x:
x + x - 9 + x - 9 = 180
x + x + x - 9 - 9 = 180
3x - 18 = 180
3x - 18 + 18 = 180 + 18
3x = 198
3x ÷ 3 = 198 ÷ 3
x = 66
Now, substitute the found value of x into the expression for ∠FCD:
m∠FCD = (x - 9)°
m∠FCD = (66 - 9)°
m∠FCD = 57°
Therefore, the measure of angle FCD is 57°.