In the parallelogram ABCD, the bisector of angle A intersects the side BC at point K.

In the parallelogram ABCD, the bisector of angle A intersects the side BC at point K. Find the degree measure of the angle AKC if the angle ADC = 144 degrees

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

2. ∠BAK = ∠DAK, since the bisector AK divides ∠A into two equal parts.

3. ∠DАК and ∠АКВ are equal as the angles formed by the parallel sides ВС and АD and the bisector AK intersecting them.

4. Consequently, ∠BAK = ∠AKB.

5. Using the property of a parallelogram that the sum of two angles adjacent to one of its sides is 180 °, we calculate the degree measure ∠A:

∠А = 180 ° – 144 ° = 36 °.

6.∠BАК = ∠АКB = 36 °: 2 = 18 °.

7.∠АКС = 180 ° – 18 ° = 162 °.

Answer: ∠АКС = 162 °.