Question

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

Answer 1

m∠DEF = 127°

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 =
`(1)/(2)(arc FGD)`

(6x + 37) =
`(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°