Answer:
x = -12
m∠FCD = 29°
Explanation:
Finding x:
- Angle BCD is comprised of angles BCF and FCD, which means the sum of their measures equals the measure of angle BCD.
Since m∠BCD = 95°, we can find x by the sum of the measures of angles BCF and FCD equal to 95:
m∠BCF + m∠FCD = m∠BCD
x + 78 + x + 41 = 95
(2x + 119 = 95) - 119
(2x = -24) / 2
x = -12
Thus, x = -12
Finding m∠FCD:
Now, we can find m∠FCD by plugging in -12 for x in x + 41:
m∠FCD = x + 41
m∠FCD = -12 + 41
m∠FCD = 29
Thus, m∠FCD = 29°