QQuestionMathematics
QuestionMathematics
By the congruent supplements theorem, what can you conclude?
A. ∠CBG≅∠DBG
B. ∠FBC≅∠DBG
C. ∠CBG is supplementary to ∠DBF
D. ∠FBC is supplementary to ∠DBG
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Answer
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Step 1:Let me solve this step by step using the congruent supplements theorem.
Step 2:: Understand the Congruent Supplements Theorem
The congruent supplements theorem states that if two angles are supplementary to the same angle, then those two angles are congruent.
Step 3:: Analyze the Supplementary Relationship
- Supplementary angles are two angles that add up to 180° - If two angles are both supplementary to the same third angle, they must be equal (congruent)
Step 4:: Evaluate the Given Options
- This means $$\angle FBC + \angle DBG = 180°
Let's carefully examine each option: - This would mean these two angles are equal - We cannot definitively conclude this from the given information - This suggests these two angles are equal - Again, insufficient information to confirm this - This is a possible conclusion, but not guaranteed - This matches the definition of the congruent supplements theorem
Final Answer
The key is recognizing that the congruent supplements theorem requires the two angles to be supplementary to the same third angle, which is satisfied by option D.
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