Final Answer:
1. ∠AOB = 30°
2. ∠COE = 83°
Step-by-step explanation:
In the given scenario, we can determine the angles ∠AOB and ∠COE using the angle addition property of a straight line.
According to this property, the sum of the angles on a straight line is always 180°. Therefore, to find ∠AOB, we subtract the given angles from 180°:
\[ ∠AOB = 180° - ∠AOE - ∠DOB \]
\[ ∠AOB = 180° - 67° - 97° \]
\[ ∠AOB = 16° \]
So, ∠AOB is 16°.
Next, to find ∠COE, we apply the same principle:
\[ ∠COE = 180° - ∠AOE \]
\[ ∠COE = 180° - 67° \]
\[ ∠COE = 113° \]
Therefore, the final values are ∠AOB = 16° and ∠COE = 113°. These results are obtained by applying the angle addition property of a straight line.
The calculation involves subtracting the given angles from 180°, resulting in the desired angles. The process is straightforward and aligns with the fundamental geometric principles governing straight lines.