Answer: the quantity in column B is greater.
Explanation:
To compare the quantity in column A with the quantity in column B, two figures are attached.
The first figure is the graph showing two intersecting lines forming four angles: two pairs of vertical angles.
The angles formed and their measures are:
- ∡DOC is vertical angle with ∡AOB so they are congruent: ∴ m∡DOC = m∡AOB = 91°.
- ∡AOD and ∡AOB are linear pair angles, so they are supplementary: m∡AOD + m∡AOB = 180° ⇒ m∡AOD = 180° - m∡AOB = 180° - 91° = 89°
- ∡COB and ∡AOD are vertical angles, so they are congruent: m∡COB = m∡AOD = 89°.
To Compare the quantity in column A with the quantity in column B, let's first summarize the results:
Angle Measure
∡AOB ≅ ∡DOC 91°
∡AOD ≅ ∡BOC 89°
The quantities to compare in column A and column B are in the second figure and they are:
Column A Column B
m∡AOD m∡DOC
89° 91° ← by substitution of above results
Conclusion: the quantity in column B is greater.
