Question

Find x and m < FCD
m < BCF = x + 78
m < FCD = x + 41
m < BCD = 95

Answer 1

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°