Compare Angles CAE and E: Geometric Relationship Analysis

Angle Comparison with Exterior Relationships

Choose the missing sign from the statement below:

Angle CAE (?) angle E.

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 Let's draw the angles
00:07 According to the drawing, we can see that angle E is larger
00:10 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

Choose the missing sign from the statement below:

Angle CAE (?) angle E.

404040404040AAABBBDDDEEECCC

2

Step-by-step solution

From the drawing, it appears that angle BAE is equal to 90 degrees, therefore it can be argued that angle CAE is less than 90 degrees.

If we look at angle E, we can see that it is greater than 90 degrees, therefore:

E>CAE E>CAE

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Exterior Angle Rule: An exterior angle equals sum of non-adjacent interior angles
  • Visual Analysis: Angle CAE appears acute (< 90°), angle E appears obtuse (> 90°)
  • Verification: Check that exterior angle E > interior angle CAE using triangle properties ✓

Common Mistakes

Avoid these frequent errors
  • Assuming angles look equal without measuring
    Don't rely only on visual appearance to compare angles = incorrect relationships! Angles can appear similar but have different measures. Always use geometric properties like the exterior angle theorem to determine precise relationships.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

How can I tell which angle is larger just by looking?

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While visual estimation helps, use geometric properties for accuracy. In this case, angle E is an exterior angle of the triangle, which must be greater than any non-adjacent interior angle like CAE.

What makes angle E an exterior angle?

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An exterior angle is formed when you extend one side of a triangle. Here, angle E is formed by extending side AE beyond point E, making it exterior to triangle ABC.

Why is angle CAE definitely less than 90 degrees?

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Looking at the figure, angle CAE appears to be an acute angle (less than 90°) because it's formed within the triangle and looks smaller than a right angle.

Can two angles in a triangle ever be equal?

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Yes! Triangles can have equal angles (like isosceles triangles with two 60° angles), but in this problem, we're comparing an interior angle with an exterior angle, which are never equal.

What if I can't tell which angle is bigger from the drawing?

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Use the exterior angle theorem: any exterior angle of a triangle is always greater than either of the non-adjacent interior angles. This gives you the answer without measuring!

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