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:

$\begin{gathered} \angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL} \\ 104=2\angle\text{BPL} \\ \angle\text{BPL}=\frac{104}{2} \\ \therefore\angle\text{BPL}=52\degree \end{gathered}$

Now,

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

Thus,

$\text{ArcLB}=52\degree$