Question

If minor arc AC = 96°, what is the measure of ∠ABC? A) 53° B) 64° C) 72° D) 84°

Answer 1

The answer is 84 d is the last answer

Answer 2

Option D

m∠ABC=
`84\°`

Explanation:

see the attached figure to better understand the problem

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

In this problem

m∠ABC is the external angle

m∠ABC=
`(1)/(2) (major\ arc\ AC- minor\ arc\ AC)`

we have

`minor\ arc\ AC=96\°`

`major\ arc\ AC=360\°-96\°=264\°`

substitute

m∠ABC=
`(1)/(2) (264\°- 96\°)=84\°`