Question

Help! Central Angles and arc measures

Answer 1

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.

Setup

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

Solution

This equation can be solved for x.

  16x +4 = 180 . . . . . . . . . . . . simplify

  16x = 176 . . . . . . . . . . . . subtract 4

  x = 11 . . . . . . . . . . . . . divide by 16