Answer:
x = 11
Step-by-step explanation:
The sum of arcs of a semicircle is 180°. That fact can be used with the given angle relations to find the value of x.
<h3>Setup</h3>
The measure of an arc is the same as the measure of the central angle it subtends.
DC +CG +GF = 180
The angle bisector CH ensures that angles CHD and CHG are congruent. That means arcs CD and CG are congruent, and we have ...
DC +DC +GF = 180 . . . . . . . . . use DC for CG
2(7x -1) +(2x +6) = 180 . . . . . . . use the given expressions
<h3>Solution</h3>
This equation can be solved for x.
16x +4 = 180 . . . . . . . . . . . . simplify
16x = 176 . . . . . . . . . . . . subtract 4
x = 11 . . . . . . . . . . . . . divide by 16
