Question

Find m/BAC

(please see attached photo)

Answer 1

∠ 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°