Question

Can you please help me out with a question

Answer 1

There are 360 degrees in a circle.

We can write:

`Arc\text{LAM}+Arc\text{MBL}=360\degree`

Given, Arc LAM = 256°, we can find Arc MBL:

`\begin{gathered} Arc\text{LAM}+Arc\text{MBL}=360\degree \\ 256+\text{ArcMBL}=360 \\ \text{ArcMBL}=360-256 \\ \text{ArcMBL}=104 \end{gathered}`

The central angle that subtends Arc MBL also measures 104 degrees.

`\angle\text{MPL}=104\degree`

We also know,

`\angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL}`

Angle MPB and Angle BPL are equal, so we have:

`\begin{gathered} \angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL} \\ 104=2\angle\text{BPL} \\ \angle\text{BPL}=(104)/(2) \\ \therefore\angle\text{BPL}=52\degree \end{gathered}`

Now,

Arc LB subtends the central angle BPL, so they are same in measure.

Thus,

`\text{ArcLB}=52\degree`