Answer: k = - 3
Step-by-step explanation:
We would apply the rule which states that vertically opposite angles are equal. It means that angle BPC and angle APD are equal because they are vertically opposite.
Therefore,
4k + 159 = 2k + 153
Subtracting 2k and 159 from the left hand side and the right hand side of the equation, it becomes
4k - 2k + 159 - 159 = 2k - 2k + 153 - 159
2k = - 6
dividing the left hand side and the right hand side of the equation by 2, it becomes
2k/2 = - 6/2
k = - 3
