Question

I need help with this, please help if you can.

Answer 1

Let's put more details in the given figure:

Step 1: Let's first find x.

The total measure of a circle is 360°.

We get,

`\text{ Arc LM + Arc MJ + Arc JR + x = 360}\degree`
`\text{ 100}\degree\text{ + 72}\degree\text{ + 140}\degree\text{ + x = 360}\degree`
`\text{ 312}\degree\text{ + x = 360}\degree`

`\text{ x = 360}\degree\text{ - 312}\degree`
`\text{ x = 48}\degree`

Step 2: Let's now find ∠K.

`\text{ m\angle K = }(1)/(2)(Arc\text{ ML - x\rparen}`
`\text{ = }(1)/(2)(72\text{ + 48\rparen = }(1)/(2)(120\degree)`
`\text{ m\angle K = 60}\degree`

Therefore, the measure of ∠K is 60°