Let

AB and
CD be two lines intersecting at point O. Let
OP be the bisector of
angle AOC,
OT the bisector of angle POB, and
OR the bisector of angle TOD. If angle POR = 25 degrees�,
find angle AOC and angle AOD.

To find the measure of angle AOC and angle AOD, we need to use the information given and some geometric properties.

First, let's analyze the information provided:
- We have two intersecting lines, AB and CD, at point O.
- We have OP as the bisector of angle AOC.
- We have OT as the bisector of angle POB.
- We have OR as the bisector of angle TOD.
- We are given that angle POR measures 25 degrees.

Now, let's break down the problem step by step:

Step 1: Find the measure of angle AOC.
To find the measure of angle AOC, we can use the property that the sum of angles around a point is 360 degrees. Since angle POR is given as 25 degrees, we can subtract this from 360 degrees to get the total angle measure around point O.

360 degrees - 25 degrees = 335 degrees.

Therefore, the measure of angle AOC is 335 degrees.

Step 2: Find the measure of angle AOD.
To find the measure of angle AOD, we need to consider the adjacent angles formed by the bisectors.
Angle POR is bisected by OR, which means it divides angle POR into two equal angles.

So, angle POR = angle ROB.
Since angle POR is given as 25 degrees, angle ROB is also 25 degrees.

Now, let's look at angle ROB, which is part of angle AOD.
Since angle ROB is bisected by OT, it divides angle ROB into two equal angles.

So, angle ROB = angle BOD.
Since angle ROB is 25 degrees, angle BOD is also 25 degrees.

Now, angle AOD can be calculated by adding all the parts:

Angle AOD = angle ROB + angle BOD
Angle AOD = 25 degrees + 25 degrees
Angle AOD = 50 degrees.

Therefore, the measure of angle AOD is 50 degrees.

In summary:
- The measure of angle AOC is 335 degrees.
- The measure of angle AOD is 50 degrees.