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In-s [12.5K]
3 years ago
11

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

Mathematics
1 answer:
Anna35 [415]3 years ago
7 0

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.

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