Finding Angle ABC: Geometric Construction with 100° Angle DBC

Reading Angles with Diagram Interpretation

Determine the size of angle ABC?

DBC = 100°

DDDBBBCCCAAA10040

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's find angle ABC.
00:10 This angle is at point B, between points A and C.
00:15 Using the given data, we can find the size of the angle.
00:20 And that's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the size of angle ABC?

DBC = 100°

DDDBBBCCCAAA10040

2

Step-by-step solution

We can see from the diagram that angle DBC equals 100 degrees.

We can also see that the size of angle ABC is shown and equals 40 degrees.

Therefore, the answer is 40.

3

Final Answer

40

Key Points to Remember

Essential concepts to master this topic
  • Diagram Reading: Extract given angle measurements and identify angle positions
  • Technique: Locate angle ABC marked as 40° in the diagram
  • Check: Verify answer matches the labeled measurement in the diagram ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle DBC with angle ABC
    Don't assume angle ABC equals angle DBC (100°) = wrong answer! These are different angles at different positions. Always read the diagram carefully to identify which specific angle is being asked for.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

Why isn't angle ABC equal to 100° like angle DBC?

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Angles ABC and DBC are different angles formed by different rays. Even though they share vertex B, they have different measurements as shown in the diagram.

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

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Look for the angle labels and degree markings in the diagram. The angle you need (ABC) should be clearly marked with its measurement.

Can I calculate angle ABC using angle DBC?

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In this problem, no calculation is needed! The diagram already shows angle ABC = 40°. Sometimes diagrams provide direct measurements rather than requiring calculations.

What if I can't see the angle measurement clearly?

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Look for small numbers near the angle arcs in the diagram. In this case, you should see 40 marked near angle ABC and 100 marked near angle DBC.

Why does the explanation seem so simple?

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Some geometry problems test your ability to read diagrams accurately rather than perform complex calculations. This is an important skill in geometry!

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