The bisector CK is drawn in an isosceles triangle AMC with a base AC. Find the angle CKM if the angle is A = 40 degrees.

1. Let us denote the angle by the symbol ∠.

2. ∠A and ∠C are equal as angles at the base of an isosceles triangle. That is, ∠С = 40 °.

3. ∠АСК = ∠С: 2 = 40 °: 2 = 20 °, since the bisector of the SC divides the angle from which it is drawn into two equal parts.

4. We calculate the value ∠ AKC:

∠ АКС = 180 – ∠ВАС – ∠АСВ = 180 ° – 40 ° – 20 ° = 120 °.

5. We calculate the value of the sought ∠CКM:

∠ SCM = 180 ° – ∠АКС = 180 ° – 120 ° = 60 °.

Answer: ∠SCM is 60 °.