Question

Pls help me with this question and if don't know, pls don't answer. thank you!

Answer 1

Answer:

m∠DEF = 127°

Step-by-step explanation:

Length of arc is double the inscribed angle formed by two chords or secants meeting at a point on the circle,

By this property,

Measure of Inscribed angle ∠DEF = $\frac{1}{2}(arc FGD)$

(6x + 37) = $\frac{1}{2}(19x-31)$

12x + 74 = 19x - 31

19x - 12x = 74 + 31

7x = 105

x = 15

Therefore, m(∠DEF) = 6(15) + 37

                                 = 90 + 37

                                 = 127°