use betweenness of rays to answer this question.

Question

If point L lies in the interior of angle AOB and the measure of angle AOL= 25, the measure of angle LOB= 55, and the measure of angle AOB= 80, then which of the following rays is between the other two: ray OB, ray OL, or ray OA?

Answer 1

To determine which ray lies between the other two, we can analyze the measures of the angles.

We know the following:

• Measure of angle AOB = 80 degrees
• Measure of angle AOL = 25 degrees
• Measure of angle LOB = 55 degrees

We can find the relationships between the rays based on the measures of these angles.

1. Measure of angle AOB: This is the total angle formed by rays OA and OB. It measures 80 degrees.

2. Measure of angle AOL + Measure of angle LOB:

   • Measure of angle AOL = 25 degrees
   • Measure of angle LOB = 55 degrees
   • Total = 25 + 55 = 80 degrees, which confirms that measurement is consistent.

3. Next, let's see which ray is between the others:

   • Since L lies in the interior of angle AOB,
   • Ray OA creates angle AOL (which is 25 degrees),
   • Ray OB creates angle LOB (which is 55 degrees).

From these angles, we can determine:

• Ray OA creates an angle of 25 degrees with the reference point (A).
• Ray OL creates an angle with ray OA of 25 degrees, leading into ray OB (the remaining angle to complete angle AOB).

Given this information, ray OL is closer to ray OA than ray OB is to ray OA.

Thus, we can conclude:

Ray OL is between ray OA and ray OB.