Comparing Angles ACB and B: Geometric Diagram Analysis

Q: How do I know which angle is angle B in the diagram?

Angle B is the angle at vertex B. Look for the small square symbol at point B - this indicates it's a right angle measuring exactly 90°.

Q: What does angle ACB mean exactly?

Angle ACB means the angle formed at vertex C, with rays going to points A and B. The middle letter (C) is always the vertex where the angle is located.

Q: Why is a right angle always 90 degrees?

A right angle is defined as exactly 90°. You can identify right angles in diagrams by the small square symbol drawn in the corner, like at point B in this problem.

Q: How do I compare angles when I see the degree measures?

Simply compare the numbers! 40° , so angle ACB is smaller than angle B. Use the symbols: (greater than), or = (equal to).

Q: What if the diagram doesn't show degree measures?

Look for visual clues like right angle squares, parallel marks, or arc symbols. You can also use geometric properties like exterior angles being larger than remote interior angles.

Angle Comparison with Right Angles

Fill in the missing sign according to the diagram:

Angle ACB (?) angle B

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing symbol

00:03 Angle size according to the given data

00:09 Angle size according to the given data, right angle equals 90

00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign according to the diagram:

Angle ACB (?) angle B

Step-by-step solution

According to the diagram, we are given that angle ACB is equal to 40 degrees.

Additionally, we are given that angle B is a right angle, meaning it is equal to 90 degrees.

Therefore:

$B > ACB$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare angle measures directly using their degree values
Technique: Identify angle ACB = 40° and angle B = 90°
Check: Since 40° < 90°, angle ACB is less than angle B ✓

Common Mistakes

Avoid these frequent errors

Confusing angle names with their positions
Don't assume angle B is smaller just because it's at the bottom corner = wrong comparison! Position doesn't determine angle size, only the degree measure matters. Always compare the actual degree values shown in the diagram.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

How do I know which angle is angle B in the diagram?

Angle B is the angle at vertex B. Look for the small square symbol at point B - this indicates it's a right angle measuring exactly 90°.

What does angle ACB mean exactly?

Angle ACB means the angle formed at vertex C, with rays going to points A and B. The middle letter (C) is always the vertex where the angle is located.

Why is a right angle always 90 degrees?

A right angle is defined as exactly 90°. You can identify right angles in diagrams by the small square symbol drawn in the corner, like at point B in this problem.

How do I compare angles when I see the degree measures?

Simply compare the numbers! 40° < 90°, so angle ACB is smaller than angle B. Use the symbols: < (less than), > (greater than), or = (equal to).

What if the diagram doesn't show degree measures?

Look for visual clues like right angle squares, parallel marks, or arc symbols. You can also use geometric properties like exterior angles being larger than remote interior angles.

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