Question

How do I solve this?

Answer 1

`/_MPL=80^o`

Explanation:

Join line `MN` and now examine `DeltaMNP`.

As `m hat(ML)=175^o` and `m hat(ON)=15^o`

`/_MPL=/_MNL-/_PMN`,

as exterior angle is equal to sum of interior opposite angles.

Now `/_MNL=1/2xx(m hat(ML))=1/2xx175^o` and

`/_PMN=1/2xx(m hat(ON))=1/2xx15^o`

Hence `/_MPL=/_MNL-/_PMN`

= `1/2xx175^o-1/2xx15^o`

= `1/2xx(175^o-15^o)`

= `80^o`

Answer 2

`angle MPL = (angle ML)/2-(angle ON)/2 = 80^o`

Explanation:

`angle OMN = (angle ON)/2`
`angle MNL = (angle ML)/2`
`angle MPL + pi-angle MNL+angle OMN=pi`
Solving for `angle MPL = (angle ML)/2-(angle ON)/2 = 80^o`