Answer:
The measure of angle RAN is 39 degrees.
Step-by-step explanation:
Given:
- AI is the angle bisector of angle KAN, and
- AR is the angle bisector of angle KAI
- angle RAK = 13 degrees
To Find:
Measure of angle RAN
Calculations:
<u>STEP 1 :</u> We note that <u>angle RAN = angle RAI + angle IAN</u> (by the construction of the angles given in the problem).
So, we need to individually find the angles RAI and IAN in order to find the angle RAN
<u>STEP 2 : Finding angle RAI</u>
Given that AR if the bisector of angle KAI, therefore angle KAR = angle RAI
Also given that angle KAR = 13 degrees.
Therefore, <u>angle RAI = 13 degrees.</u>
<u>STEP 3 : Finding angle IAN</u>
Given that AI is the bisector of angle KAN, therefore angle KAI = angle IAN
Now,
angle KAI = angle KAR + angle RAI
= 13 + 13 degrees (using what we found out in STEP 1)
= 26 degrees
Therefore <u>angle IAN = angle KAI = 26 degrees</u>
<u>STEP 4 : Finding angle RAN</u>
As we noted in STEP 1,
angle RAN = angle RAI + angle IAN
= 13 + 26 degrees (using Steps 2 and 3)
= 39 degrees
<u>Therefore, angle RAN = 39 degrees</u>
<u><em>NOTE - A hand-drawn diagram has been attached so that it is easier to picture the solution. I hope this helps!</em></u>