Answer:
A linear pair is two angles that are adjacent to each other and forms a line.
Supplementary Angle: If any two angles form a linear pair, then they are supplementary(i.e, 180 degree).
From the given figure, [tex]100^{\circ}[/tex] and [tex]n^{\circ}[/tex] forms a linear pair.
Also, if the two angles are linear pair, then they are supplementary angle.
then,
[tex]100^{\circ}+n^{\circ}=180^{\circ}[/tex]
Simplify:
[tex]n = 180-100=80^{\circ}[/tex]
Vertical opposite angle theorems states about the two angles that are opposite to each other and are equal also.
From the figure, [tex]p^{\circ}[/tex] and [tex]95^{\circ}[/tex] are vertical opposite angle.
therefore, [tex]p=95^{\circ}[/tex]
Now, to find the value of m;
Sum of the measures of the interior angles of a polygon with 4 sides is 360. degree.
here, [tex]n^{\circ}[/tex], [tex]p^{\circ}[/tex] , [tex]m^{\circ}[/tex] and [tex]90^{\circ}[/tex] forms a qudrilateral.
therefore, by definition:
[tex]n^{\circ}+p^{\circ}+m^{\circ}+90^{\circ}=360^{\circ}[/tex]
Substituting the values of [tex]p=95^{\circ}[/tex] and [tex]n=80^{\circ}[/tex] we have;
[tex]80+95+m^{\circ}+90^{\circ} = 360^{\circ}[/tex] or
[tex]265^{\circ}+m^{\circ}=360^{\circ}[/tex]
Simplify:
[tex]m^{\circ}=360^{\circ}-265^{\circ}=95^{\circ}[/tex]
Therefore, the value of [tex]n=80^{\circ}[/tex] , [tex]p=95^{\circ}[/tex] and [tex]m=95^{\circ}[/tex]
