Question

The size of angle aob is equal to 132 degrees and the size of angle cod is equal to 141 degrees. find the size of angle dob.

Answer 1

angle AOB = 132 and is also the sum of angles AOD and DOB. Hence 
angle AOD + angle DOB = 132°    ---> 1 

angle COD = 141 and is also the sum of angles COB and BOD. Hence 
angle COB + angle DOB = 141°    ---> 2

Now we add the left sides together and the right sides of equations 1 and 2 together to form a new equation. 

angle AOD + angle DOB + angle COB + angle DOB = 132 + 141       ---> 3 

We should also note that: 
angle AOD + angle DOB + angle COB = 180° 

Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180 and solving for angle DOB:
180 + angle DOB = 132 + 141 
angle DOB = 273 - 180 = 93°