Find the angle at point $K$. Given that the angle at point $M$ is $60^\circ$ and the angle at point $P$ is $40^\circ$. Also, the line through $K$ is parallel to the line through $M$.

1. Problem Description

Find the angle at point $K$. Given that the angle at point $M$ is $60^\circ$ and the angle at point $P$ is $40^\circ$. Also, the line through $K$ is parallel to the line through $M$.

2. Solution Steps

Since the line through $K$ is parallel to the line through $M$, the angle $KMP$ is the same as the angle at $K$ on the side $KM$. Let's call the angle at $M$ $a$.

Then, the angle $a=60^\circ$.

In triangle $KMP$, the sum of angles is $180^\circ$. Therefore,

$a + \angle P + \angle K = 180^\circ$

$60^\circ + 40^\circ + \angle K = 180^\circ$

$100^\circ + \angle K = 180^\circ$

$\angle K = 180^\circ - 100^\circ$

$\angle K = 80^\circ$

3. Final Answer

The angle at K is 80 degrees.