In the parallelogram ABCD, the angle A is 54. Find the value of the angle CKA if SC is the bisector of the angle DCB.

1. Let us denote the angle by the symbol ∠. Point K is on the AD side.

2. In a parallelogram (according to its properties) the angles opposite each other are equal.

That is, ∠А = ∠С = 54 °.

3. We calculate the degree measure ∠DCК, taking into account that the bisector ∠С divides it into two equal angles:

∠DCК = ∠С: 2 = 54 °: 2 = 27 °.

4.∠D = 180 – ∠A = 180 ° – 54 ° = 126 °.

5.∠CКD = 180 ° – ∠СDК – ∠DCК = 180 ° – 126 ° – 27 ° = 27 °.

6. ∠АКС = 180 ° – ∠СКD = 180 ° – 27 ° = 153 °.

Answer: ∠АКС = 153 °.