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 = [tex]\frac{1}{2}(arc FGD)[/tex]
(6x + 37) = [tex]\frac{1}{2}(19x-31)[/tex]
12x + 74 = 19x - 31
19x - 12x = 74 + 31
7x = 105
x = 15
Therefore, m(∠DEF) = 6(15) + 37
= 90 + 37
= 127°
