Compare Angles: Determining the Relationship Between Angle B and ACD in a 40° Parallel Line System

Q: How do I know angle B is exactly 90 degrees?

The small square symbol at point B indicates a right angle, which is always exactly $ 90° $. This is a standard geometric notation.

Q: What does supplementary angles mean?

Supplementary angles add up to $ 180° $. When you see angles on a straight line, they're supplementary: $ \angle ACB + \angle ACD = 180° $.

Q: Why can't I just estimate from the diagram?

Diagrams can be misleading and not drawn to scale. Always use the given angle measures and geometric relationships to calculate exact values for accurate comparisons.

Q: How do I calculate angle ACD step by step?

Since angles ACB and ACD are supplementary:$ 40° + \angle ACD = 180° $$ \angle ACD = 180° - 40° = 140° $

Q: What if the angles were equal instead?

If both angles measured the same, you'd use the equals sign (=). But here, \( 90° , so angle B is less than angle ACD.

Parallel Line Angles with Interior Calculations

Fill in the missing sign according to the diagram:

Angle B (?) angle ACD

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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 According to the given data, a right angle equals 90

00:09 Supplementary angle on the line, supplements to 180 therefore it's larger

00:14 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 B (?) angle ACD

Step-by-step solution

According to the diagram, angle B is a right angle equal to 90 degrees.

If we look at angle ACD, we can see that it is larger than 90 degrees.

We can also calculate angle ACD since it is supplementary to 180 degrees:

$180=ACB+ACD$

$180=40+ACD$

$180-40=ACD$

$140=ACD$

Therefore:

$90 > 40$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Right Angles: Angle B is 90° shown by square symbol
Supplementary Angles: ACB + ACD = 180°, so 40° + ACD = 180°
Check: Compare calculated values: 90° < 140°, so angle B < angle ACD ✓

Common Mistakes

Avoid these frequent errors

Comparing angles without calculating exact measures
Don't just guess by looking at the diagram = wrong comparisons! Visual estimates can be misleading, especially with obtuse angles. Always calculate the exact degree measures using angle relationships like supplementary pairs.

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 angle B is exactly 90 degrees?

The small square symbol at point B indicates a right angle, which is always exactly $90°$ . This is a standard geometric notation.

What does supplementary angles mean?

Supplementary angles add up to $180°$ . When you see angles on a straight line, they're supplementary: $\angle ACB + \angle ACD = 180°$ .

Why can't I just estimate from the diagram?

Diagrams can be misleading and not drawn to scale. Always use the given angle measures and geometric relationships to calculate exact values for accurate comparisons.

How do I calculate angle ACD step by step?

Since angles ACB and ACD are supplementary:

$40° + \angle ACD = 180°$
$\angle ACD = 180° - 40° = 140°$

What if the angles were equal instead?

If both angles measured the same, you'd use the equals sign (=). But here, $90° < 140°$ , so angle B is less than angle ACD.

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