Answer:
A. Parallelogram LMNP
B. 33
C. 98°
Step-by-step explanation:
LMNP is a parallelogram.
Adjacent angles of a parallelogram are Supplementary.
[tex] \therefore 82\degree +(3x - 1)\degree =180\degree [/tex]
[tex] \therefore (3x - 1+82)\degree =180\degree [/tex]
[tex] \therefore (3x +81)\degree =180\degree [/tex]
[tex] \therefore 3x +81 =180 [/tex]
[tex] \therefore 3x =180-81 [/tex]
[tex] \therefore 3x =99 [/tex]
[tex] \therefore x =\frac{99}{3} [/tex]
[tex] \therefore x =33 [/tex]
[tex] \implies m\angle N= (3x - 1)\degree=(3*33 - 1)\degree=(99-1)\degree = 98\degree [/tex]
[tex] \because m\angle L =m\angle N[/tex]
(Opposite angles of a parallelogram)
[tex] \therefore m\angle L =98\degree [/tex]
