The measure of angle ANC is 60 degrees
From the diagram, we have the following parameters
[tex]\angle ABC = 20[/tex]
[tex]\angle CAB = 80[/tex]
How to calculate angle ANC
Given that triangle ABC is an isosceles triangle, where lengths AB and BC are congruent, then
[tex]\angle BCA = 80[/tex] ---- the base angles of an isosceles triangle
Line C N divides angle B CA into equal halves.
So, we have:
[tex]\angle Z C N = \frac 12 \times \angle B C A[/tex]
[tex]\angle Z C N = \frac 12 \times 80[/tex]
[tex]\angle Z C N = 40[/tex]
Considering triangle ANC, we have:
[tex]\angle Z C N + \angle CAN + \angle ANC = 180[/tex] --- the sum of angles in a triangle
So, we have:
[tex]40 + 80 + \angle ANC = 180[/tex]
[tex]120 + \angle ANC = 180[/tex]
Subtract 120 from both sides
[tex]\angle ANC = 60[/tex]
Hence, the measure of angle ANC is 60 degrees
Read more about isosceles triangles at:
https://brainly.com/question/1475130
