Find Angle BCD: Complex Geometric Figure with 90° Perpendicular Angles

Q: How do I know which angles to add together?

Look at the path from one ray to another! For angle BCD, trace from ray CB to ray CD and identify all the consecutive angles along that path: BCF, FCE, and ECD.

Q: What if I can't see all the angle measurements clearly?

Use the given information in the problem statement! Sometimes angles are described in text rather than labeled directly on the diagram. Match each description to its location.

Q: Can I subtract angles instead of adding them?

Yes! If you have a larger angle and need to find a smaller part, subtract the unwanted portions. For example: $ ∠BCD = ∠BCE - ∠ECD $ if E is between C and D.

Q: Why can't I just use the angles that look biggest?

Angle size in diagrams can be misleading! Always use the numerical values given, not visual appearance. A 10° angle might look bigger than a 40° angle depending on how it's drawn.

Q: What if the rays don't form a straight line?

That's fine! Angle addition works for any configuration of rays. Just make sure you're following the correct path from the first ray to the last ray through all intermediate rays.

Angle Addition with Composite Segments

It is known that angles A and D are equal to 90 degrees

Angle BCE is equal to 55 degrees

Angle DEB is equal to 95 degrees

Angle FCD is equal to 50 degrees

Complete the value of angle BCD based on the data from the figure.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:18 Let's find the angle, BCD.

00:21 Angle C, is the space between points B and D. Let's take a closer look!

00:28 Remember, the whole angle is just the sum of its smaller parts.

00:46 Now, we'll plug in the right numbers, based on what we have, and solve to find the angle!

01:08 And there you have it! That's how we solve the problem of finding angle BCD.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

It is known that angles A and D are equal to 90 degrees

Angle BCE is equal to 55 degrees

Angle DEB is equal to 95 degrees

Angle FCD is equal to 50 degrees

Complete the value of angle BCD based on the data from the figure.

Step-by-step solution

Let's look at angle BCD and break it down into the angles that compose it:

$BCD=BCF+FCE+ECD$

Note that the angle values we wrote in the formula are given to us in the diagram, and now we'll substitute them:

$BCD=25+30+20$

$BCD=75$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Break complex angles into smaller, measurable component angles
Technique: $BCD = BCF + FCE + ECD = 25 + 30 + 20$
Check: Verify all component angles are clearly labeled in diagram ✓

Common Mistakes

Avoid these frequent errors

Adding wrong angle segments
Don't randomly add any angles you see in the diagram = wrong total! This ignores the actual path from ray CB to ray CD. Always trace the exact path and identify only the consecutive angles that form the target angle.

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 angles to add together?

Look at the path from one ray to another! For angle BCD, trace from ray CB to ray CD and identify all the consecutive angles along that path: BCF, FCE, and ECD.

What if I can't see all the angle measurements clearly?

Use the given information in the problem statement! Sometimes angles are described in text rather than labeled directly on the diagram. Match each description to its location.

Can I subtract angles instead of adding them?

Yes! If you have a larger angle and need to find a smaller part, subtract the unwanted portions. For example: $∠BCD = ∠BCE - ∠ECD$ if E is between C and D.

Why can't I just use the angles that look biggest?

Angle size in diagrams can be misleading! Always use the numerical values given, not visual appearance. A 10° angle might look bigger than a 40° angle depending on how it's drawn.

What if the rays don't form a straight line?

That's fine! Angle addition works for any configuration of rays. Just make sure you're following the correct path from the first ray to the last ray through all intermediate rays.

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