Question

In the figure, m KL=114° and LN=56° what is the measure of

Answer 1

Let's put more details in the given figure.

From the figure shown, it appears that Arc KM, Arc KL and Arc LN covers half of the circle.

Thus, the total sum of the three mentioned arcs is 180°.

For us to find the measure of ∠LJN, let's first determine the measure of Arc KM.

We get,

`\text{ Arc KM + Arc KL + Arc LN = 180}\degree`
`\text{ Arc KM + 114}\degree\text{ + 56}\degree\text{ = 180}\degree`
`\text{ Arc KM + 170}\degree\text{ = 180}\degree`
`\text{ Arc KM = 180}\degree\text{ - 170}\degree`
`\text{ Arc KM = 10}\degree`

Therefore, the measure of Arc KM is 10°.

Let's now determine the measure of ∠LJN.

For this, the following equation will be applied.

In this problem, the formula will be:

`\text{ \angle LJN = }(1)/(2)(\text{ Arc LN - Arc KM\rparen}`
`\text{ \angle LJN = }(1)/(2)(56^(\degree)\text{ - 10}\degree)\text{ = }(1)/(2)(46\degree)`
`\text{ \angle LJN = 23}\degree`

Therefore, the measure of ∠LJN is 23°