Question

Help I’m so confused

Answer 1

The measure of arc AC is
`136^o`

Explanation:

Notice that angle BAC (whose measure is given as 34 degrees) is an inscribed angle, and according toe the inscribed angle theorem, the measure of an inscribed angle is half the measure of the central angle that subtends the same chord.

Then, the central angle that subtends the cord BC, is twice 34 degrees (
`2\,*\,34^o = 68^o`)

Then, since they give us also the measure of the arc AB which is
`156^o`, then the measure of arc AC can be estimated as the needed measure to complete
`360^o` as the sum of all three arcs. That is:

`AC + AB+ BC = 360^o\\AC + 156^o+2\,*\,34^o = 360^o\\AC + 156^o+68^o = 360^o\\AC=360^o-156^o-68^o\\AC=136^o`