Help! Central Angles and arc measures

Mathematics

1 answer:

enot [183]1 year ago

6 0

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

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