Compare Angles BAC and BAE: Geometric Relationship Analysis

Angle Addition with Geometric Reasoning

Fill in the missing sign according to the diagram:

Angle BAC (?) angle BAE

404040404040AAABBBDDDEEECCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the missing sign
00:03 Cannot determine the size of BAC
00:09 Must be larger because the second angle is part of it
00:16 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing sign according to the diagram:

Angle BAC (?) angle BAE

404040404040AAABBBDDDEEECCC

2

Step-by-step solution

From the diagram, we can see that we don't know the size of angle BAC.

However, we should be able to work out that angle BAE is equal to BAC+CAE BAC+CAE .

This means that angle BAE must be larger than angle BAC, since we are adding another angle to find its value.

Therefore:

BAE>BAC BAE>BAC

3

Final Answer

> >

Key Points to Remember

Essential concepts to master this topic
  • Angle Addition: BAE = BAC + CAE when rays are ordered
  • Visual Analysis: Point E is between C and D on line AE
  • Verification: Larger angle contains smaller angle plus additional angle ✓

Common Mistakes

Avoid these frequent errors
  • Trying to measure angles without understanding their relationship
    Don't attempt to calculate exact angle measures when given limited information = unnecessary work! The diagram shows angle relationships, not specific measurements. Always use angle addition properties to compare angles logically.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

How can I compare angles without knowing their exact measurements?

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You can use angle relationships! When one angle is part of another (like BAC is part of BAE), the larger angle will always be greater than the smaller one.

What does it mean that BAE = BAC + CAE?

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This means angle BAE is made up of two parts: angle BAC plus angle CAE. Since we're adding a positive angle to BAC, the result (BAE) must be larger.

Do I need to use the 40° markings in the diagram?

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No! The 40° angles show this is a rectangle, but they don't affect the comparison between angles BAC and BAE. Focus on the angle addition relationship instead.

How do I know which angle is inside the other?

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Look at the rays! Ray AC is between rays AB and AE, so angle BAC is contained within the larger angle BAE.

What if the angles looked equal in the diagram?

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Never rely on visual appearance alone! Use mathematical reasoning. Since BAE = BAC + CAE and CAE is a positive angle, BAE must be greater than BAC.

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