Answer:
[tex]\angle L = 52\\\\\angle J = 45\\\\\angle K = 83[/tex]
Step-by-step explanation:
[tex]\angle J = \angle L-7\\\\\angle K=2\angle L-21\\\\\angle L = \angle L[/tex]
we know that
[tex]\angle K +\angle J + \angle L =180[/tex] by the sum of interior angles of a triangle
so we have
[tex](\angle L -7)+(2\angle L -21)+(\angle L)=180[/tex]
we can simplify
[tex](\angle L + 2\angle L + \angle L)+(-7-21)=180\\\\4\angle L -28=180\\\\4\angle L=180+28\\\\4\angle L = 208\\\\\angle L = 52[/tex]
and now we find the other angles
[tex]\angle J = \angle L -7\\\\=52-7\\\\=45[/tex]
[tex]\angle K = 2\angle L -21\\\\=2(52)-21\\\\=104-21\\\\=83[/tex]
