Final Answer:
When a triangle has a reflex angle, the other two angles are called non-reflex. In this case, the non-reflex angle dob measures 146.5 degrees when the reflex angle dob is known to be 360 degrees minus the sum of both angles.
Explaination:
In a triangle, the sum of the angles is 180 degrees. When one angle is a reflex angle (greater than 180 degrees), the other two angles are called non-reflex angles. In this case, we have two non-reflex angles, dob and aod, and a reflex angle, dob.
Let's call the reflex angle dob and the non-reflex angle dob in degrees d. The other non-reflex angle aod is also in degrees y.
The sum of the angles is:
d + d + y = 180 degrees
Substituting d = 360 - (d + y):
360 - (d + y) + d + y = 180 degrees
Simplifying:
2d = 180 degrees
d = 90 degrees (non-reflex angle dob)
Substituting d = 90 degrees in the first equation:
90 + y + (360 - (90 + y)) = 180 degrees
Simplifying:
y = 60 degrees (aod)
The measure of the non-reflex angle dob in degrees is:
dob = 360 - (90 + 60) = 146.5 degrees.