Question

Given: ∠JOH = 27° and arc NML = 98°. Find the measure of arc JH.

Answer 1

∠JOH = 1/2(arc NML - arc JH)
27 = 1/2(98 - arc JH)
54 = 98 - arc JH
arc JH = 98 - 54
arc JH = 44

Answer
mJH = 44°

Answer 2

The measure of arc JH is 44°.

Explanation:

Given information: ∠JOH = 27° and arc NML = 98°.

If two chord intersect outside the circle, then

`\frac{\text{major arc-minor arc}}{2}=\text{Angle between of chords}`

From the given figure it is clear that the major arc is NML and the minor arc is JH.

Let the measure of arc JH be x.

`\frac{\text{arc NML-arc JH}}{2}=\angle JOH`

`(98-x)/(2)=27`

`98-x=54`

`-x=-44`

`x=44`

Therefore the measure of arc JH is 44°.