Respuesta :
Answer:
[tex]m \angle \ DE\ F = 127\°[/tex]
Step-by-step explanation:
Given:
[tex]m \angle \ DE\ F = (6x+37)[/tex]
[tex]m \ arc \ FGD = (19-31)[/tex]
We need to find the m ∠ DEF.
Solution:
Now we can say that;
By inscribed angle theorem;
"The measure of the angle is twice the measure on the arc subtended by it."
so we get;
[tex]2 \ m \angle DE\ F = m\ arc \ FGD[/tex]
[tex]2(6x+37)= 19x-31[/tex]
Applying distributive property we get;
[tex]12x+74=19x-31[/tex]
Combining the like terms we get;
[tex]19x-12x=74+31\\\\7x = 105[/tex]
Dividing both side by 7 we get;
[tex]\frac{7x}{7}=\frac{105}{7}\\\\x=15[/tex]
[tex]m \angle \ DE\ F = (6x+37) = (6\times 15+37) = 90+37 =127\°[/tex]
Hence [tex]m \angle \ DE\ F = 127\°[/tex]
