Compare Angles D and ACB: Geometric Diagram Analysis with 40° Measurements

Q: How do I know which angles to compare?

Look for the angle labels mentioned in the question. Here we need to compare 'angle D' and 'angle ACB' - find these specific angles in the diagram and read their measurements.

Q: What does angle ACB mean?

Angle ACB means the angle at vertex C, formed by rays CA and CB. The middle letter (C) is always the vertex of the angle.

Q: Are angles D and ACB really the same if they look different?

Yes! Angle size depends only on the degree measurement, not on how the angle looks or where it's positioned. Both angles measure 40°, so they are equal.

Q: What symbol should I use for equal angles?

Use the equals sign (=) when comparing angles with the same measurement. Since both angles are 40°, write: angle D = angle ACB.

Q: Could the angles be different even if they both say 40°?

No! If two angles are both labeled as 40°, they are definitely equal. The degree measurement is the exact size of the angle - there's no guessing involved.

Angle Comparison with Equal Angle Measurements

According to the diagram, fill in the missing sign:

Angle D ? angle ACB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing sign

00:04 Angle size according to the given data

00:10 Angle size according to the given data

00:15 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

According to the diagram, fill in the missing sign:

Angle D ? angle ACB.

Step-by-step solution

We can observe from the drawing that angle D is equal to 40 degrees,

We are also given that angle ACB is equal to 40 degrees. Therefore:

$D=ACB$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Equal Angles: When two angles have identical degree measures, they are equal
Reading Diagrams: Both angle D and angle ACB are marked as 40°
Verification: Compare given measurements: 40° = 40° confirms angles are equal ✓

Common Mistakes

Avoid these frequent errors

Assuming angle position affects size
Don't think angles in different positions must be different sizes = wrong comparison! Position doesn't change an angle's measurement - only the degree value matters. Always compare the actual degree measurements, not where the angles appear in the diagram.

Practice Quiz

Test your knowledge with interactive questions

a is parallel to b.

Calculate the angles shown in the diagram.

FAQ

Everything you need to know about this question

How do I know which angles to compare?

Look for the angle labels mentioned in the question. Here we need to compare 'angle D' and 'angle ACB' - find these specific angles in the diagram and read their measurements.

What does angle ACB mean?

Angle ACB means the angle at vertex C, formed by rays CA and CB. The middle letter (C) is always the vertex of the angle.

Are angles D and ACB really the same if they look different?

Yes! Angle size depends only on the degree measurement, not on how the angle looks or where it's positioned. Both angles measure 40°, so they are equal.

What symbol should I use for equal angles?

Use the equals sign (=) when comparing angles with the same measurement. Since both angles are 40°, write: angle D = angle ACB.

Could the angles be different even if they both say 40°?

No! If two angles are both labeled as 40°, they are definitely equal. The degree measurement is the exact size of the angle - there's no guessing involved.

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