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Leviafan [203]
2 years ago
15

Help! Central Angles and arc measures

Mathematics
1 answer:
enot [183]2 years 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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Then the number of right handed female students will be 5x and the number of right handed male students will be 9y. Since the total number of left handed students is 18 and the total number of right handed students is 122, the following system of equations must be satisfied.

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