Question

Find m/BAC if arc AB = 133° and arc AC = 99°.

mAngleA = ??? Degrees

Answer 1

∠BAC = 64°

Explanation:

First, we should know that a circles' diameter equals 360°, meaning that the arcs combined sum will equal 360°.

Find mBC (x):

133° + 99° + x° = 360°

232° + x° = 360°

x° = 128°

Inscribed angles, such as ∠BAC, are half of the arc they are shown to have points outside of. (C and B)

∠BAC =
`(1)/(2)`(mBC)

∠BAC = 64°