Question

PLEASE HELP ME!

Find m∠FEC.

Answer Options:
A. 69
B. 50
C. 57
D. 37

Answer 1

Option (A)

Explanation:

Measure of an angle formed between a chord and a secant is equal to the half of the difference of the intercepted arcs.

m(∠FEC) =
`(1)/(2)[m(\text{arc FC})-m(\text{arc})FD]`

(15 + 6x)° =
`(1)/(2)[(24x - 6)^(\circ)-(9+7x)^(\circ)]`

30 + 12x = (24x - 7x) - (6 + 9)

30 + 12x = 17x - 15

17x - 12x = 30 + 15

5x = 45

x = 9

m(∠FED) = (15 + 6x)

= 15 + 6(9)

= 69°

Option (A) will be the correct option.