Answer:
x = 52°
Explanation:
Given various inscribed angles in a circle, you want the measure of central angle x.
Inscribed angles
The inscribed angle theorem tells you an arc is double the measure of the inscribed angle it subtends:
arc JKM = 2·80° = 160°
arc JNL = 2·126° = 252°
Arcs of a circle
The sum of arcs around a circle is 360°. This tells you ...
arc JKL = 360° -252° = 108°
An arc has a measure equal to the sum of its parts, so ...
arc JKM = arc LM +arc JKL
160° = x + 108°
x = 52° . . . . . . . . . . subtract 108°