Question

Question 10 of 14 VIn the figure, CJ and CR are opposite rays. CP bisects NCW and CL bisects LJCN.RWIf MZICN = 8r – 2 and mZLCN = 3r + 15, find mZICL.

Answer 1

From the diagram, we can see that CL bisects angle JCN. This means that CL divides the angle JCN into 2 equal halves. It means that

angle JCN = angle JCL + angle LCN

Given that angle JCN = 8r - 2 and angle LCN = 3r + 15, it means that

8r - 2 = angle JCL + 3r + 15

Since angle JCL = angle LCN, then

8r - 2 = 3r + 15 + 3r + 15

8r - 2 = 6r + 30

8r - 6r = 30 + 2

2r = 32

r = 32/2

r = 16

angle JCL = 3r + 15 = 3 * 16 + 15

angle JCL = 48 + 15

angle JCL = 63 degrees