The angles K and D shown in the parallel line cut by a transversal are same side interior angles (option B)
How to determine the relationship of angle K and D
To determine the correct answer to the question, we shall apply the transversal theorem. This is shown below:
According to the transversal theorem, the following are observed from the diagram provided:
- Angle A + Angle B = 180 (angle on a straight line)
- Angle A + Angle K = 180 (angle on a straight line)
- Angle K + Angle C = 180 (angle on a straight line)
- Angle B + Angle C = 180 (angle on a straight line)
- Angle A = Angle C (vertically opposite angles)
- Angle K = Angle B (vertically opposite angles)
- Angle C = Angle D (alternate angles)
- Angle K = Angle D (same side interior angles)
- Angle A = Angle D (corresponding angles)
From the above information, we can see that angle K and angle D are same side interior angles
Thus, the correction answer is option B