Question

For the following figure, $\angle KAP$is a right angle and $\overline{AM}$is a median then complete the statement

If $m\angle K=40$then $m\angle KAM=\_\_$.

Short answer

The statement is “if $m\angle K=40$, then $m\angle KAM=40$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

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

Here the angle KAP is a right-angle triangle.

Step 3. Step description.

Now, simplify the figure as follows:

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

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

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

Thus, the statement is $m\angle KAM=40$.