Question

PLEASE HELP ME! Find m∠FEC. Answer Options: A. 69 B. 50 C. 57 D. 37

Answer 1

Answer:

Option (A)

Step-by-step 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) = $\frac{1}{2}[m(\text{arc FC})-m(\text{arc})FD]$

(15 + 6x)° = $\frac{1}{2}[(24x - 6)^{\circ}-(9+7x)^{\circ}]$

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.