Final answer:
To find the missing measures of triangle MNP given that point C is the incenter, we can use the properties of the incenter. The angle bisectors of the triangle divide the angles into congruent angles.
Step-by-step explanation:
The incenter of a triangle is the point of concurrency of the angle bisectors of the triangle. In this case, we are given that point C is the incenter of triangle MNP.
To find the missing measures, we need to use the properties of the incenter. The angle bisectors of triangle MNP divide the angles into two congruent angles.
Let's say the measure of angle MCP is x. Since point C is the incenter, angle MCP is divided into two congruent angles by the angle bisector CM. So, each of these angles has a measure of x/2. Similarly, angle MNP is divided into two congruent angles by the angle bisector CN.
Therefore, the missing measures are:
- Measure of angle MCP: x
- Measure of angle CNP: x/2
- Measure of angle MCN: x/2