Answer:
Given that,
In circle,
measure of angle DGE is 52 degrees
[tex]m(arcDE)=(4x+39)\degree[/tex]
To solve for x,
we know that,
The angle formed by the two secants that intersect on the circle is half of the intercepted arcs.
Using this we get,
[tex]\angle DGE=\frac{1}{2}(arc(DE))[/tex]
Substitute the values we get,
[tex]52\degree=\frac{(4x+39)\degree}{2}[/tex][tex]104=4x+39[/tex][tex]4x=104-39[/tex][tex]4x=63[/tex][tex]x=\frac{63}{4}[/tex][tex]x=15.75[/tex]
Round the answer to the nearest tenth.
[tex]x=15.8[/tex]
Answer is:
[tex]x=15.8[/tex]
