SOLUTION: JKLMN is a regular pentagon and the diagonals JL and JM are joined. Because of the symmetry of the pentagon, all three triangles are isosceles, and the left and right triangles are

Algebra ->  Polygons -> SOLUTION: JKLMN is a regular pentagon and the diagonals JL and JM are joined. Because of the symmetry of the pentagon, all three triangles are isosceles, and the left and right triangles are      Log On


   

Question 976152: JKLMN is a regular pentagon and the diagonals JL and JM are joined. Because of the symmetry of the pentagon, all three triangles are isosceles, and the left and right triangles are congruent.
a) Calculate angle JNM.
b) Calculate angles NMJ and NJM.
c) What is the size of angle NML?
d) Calculate angles JML and JLM.
e) Calculate angle MJL.
Give a reason at each step.
Found 2 solutions by solver91311, FrankM:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


What have you done to try to solve this for yourself?

John

My calculator said it, I believe it, that settles it

Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
.
The single angles, N, K are each 108. 3 triangles must add to 180*3=540, then divide by 5.
a) 108
b) Since JKL is isosceles, we take 180-108=72 and divide 72/2 = 36 each
c) also 108
d) NML is 108 and NMJ is 36 so 108-36=72 each
e) 180-144=36