Question

If ray AI is the angle bisector of angle KAN and ray AR is the angle bisector of angle KAI, what is the measure of angle RAN if the measure of angle RAK= 13 degrees?

I have this question and I need it answered quickly because it's due in two days!!!!

Answer 1

The measure of angle RAN is 39 degrees.

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:

STEP 1 : We note that angle RAN = angle RAI + angle IAN (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

STEP 2 : Finding angle RAI

Given that AR if the bisector of angle KAI, therefore angle KAR = angle RAI

Also given that angle KAR = 13 degrees.

Therefore, angle RAI = 13 degrees.

STEP 3 : Finding angle IAN

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 angle IAN = angle KAI = 26 degrees

STEP 4 : Finding angle RAN

As we noted in STEP 1,

angle RAN = angle RAI + angle IAN

= 13 + 26 degrees (using Steps 2 and 3)

= 39 degrees

Therefore, angle RAN = 39 degrees

NOTE - A hand-drawn diagram has been attached so that it is easier to picture the solution. I hope this helps!