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Find m/BAC

(please see attached photo)

Find m/BAC (please see attached photo)-example-1
User Rattray
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1 Answer

2 votes

Answer:

∠ BAC = 54°

Explanation:

the chord- chord angle BAC is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

∠ BAC =
(1)/(2) (BC + FD ) , that is

10x + 4 =
(1)/(2) (12x + 15 + 9x - 12)

10x + 4 =
(1)/(2) (21x + 3) ← multiply both sides by 2 to clear the fraction

20x + 8 = 21x + 3 ( subtract 21x from both sides )

- x + 8 = 3 ( subtract 8 from both sides )

- x = - 5 ( multiply both sides by - 1 )

x = 5

Then

∠ BAC = 10x + 4 = 10(5) + 4 = 50 + 4 = 54°

User Nbar
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