Chapter 5.4, Problem 10CE

To determine

To find: The angle KAM .

Answer to Problem 10CE

The angle KAM is $40$ .

Explanation of Solution

Given:

The triangle is shown below:

  

The angle KAP is right angle. AM is the median. The angle K is $40$ .

Calculation:

For the right angle triangle, median is equal to one half of the hypotenuse.

Hence,

  $\begin{array}{c}AM=\frac{KP}{2}\\ AM=\frac{2MK}{2}\\ AM=MK\end{array}$

Now, opposite angles of equal sides must be equal for triangle MKA .

  $\begin{array}{c}m\angle K=m\angle KAM\\ m\angle KAM=40\end{array}$

Thus, the angle KAM is $40$ .