How do I solve this?

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2 Answers
May 16, 2016

#/_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#

May 16, 2016

#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 #