Question

AB and CD are straight line segments. AOE = 67° and DOB = 97°. Find the values of the following angles giving a reason for each answer.

Answer 1

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.