Calculate Angle BCE: Complex Figure with 90° and 95° Angles

Q: Why don't I need the 90° and 95° angles given in the problem?

Those angles help define the shape of the figure, but BCE is formed by combining two specific segments shown in the diagram. The directly labeled angles 25° and 30° are what you need.

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

Look for angles that are adjacent (share a common ray) and together form the angle you're finding. In this case, BCF and FCE are next to each other and together make BCE.

Q: What if the diagram shows different angle measures?

Always use the numbers shown in the diagram for your calculations. The angle measures given in the problem text (like 90° and 95°) provide context but may not be the ones you directly calculate with.

Q: Can I solve this problem without the diagram?

No, the diagram is essential because it shows which specific angle segments combine to form BCE. Without seeing the geometric relationships, you can't determine the correct angle addition.

Q: What does angle addition mean in geometry?

Angle addition means that when two angles share a common vertex and ray, their measures add up to form a larger angle. It's like: $ \text{whole angle} = \text{part 1} + \text{part 2} $

Angle Addition with Geometric Decomposition

Angles A and D are both equal to 90 degrees.

Angle DEB is equal to 95 degrees.

Calculate the value of angle BCE based on the data in the figure.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find angle BCE

00:03 Angle C between points B and E

00:13 The total angle equals the sum of its parts

00:32 Let's substitute the angle values and solve for angle BCE

00:49 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

Angles A and D are both equal to 90 degrees.

Angle DEB is equal to 95 degrees.

Calculate the value of angle BCE based on the data in the figure.

Step-by-step solution

Let's break down angle BCE into an angle addition exercise:

$BCE=BCF+FCE$

Now let's input the known data from the diagram:

$BCE=25+30$

$BCE=55$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Break complex angles into simpler component angles that add together
Technique: Identify BCE = BCF + FCE = 25° + 30° = 55°
Check: Verify angle measurements align with given constraints and diagram ✓

Common Mistakes

Avoid these frequent errors

Trying to use the 90° and 95° angles directly
Don't attempt to calculate BCE using angles A, D, or DEB = confusing results! These angles constrain the figure but don't directly form BCE. Always identify which specific angle segments actually combine to form the target angle.

Practice Quiz

Test your knowledge with interactive questions

Find the measure of the angle $\alpha$

FAQ

Everything you need to know about this question

Why don't I need the 90° and 95° angles given in the problem?

Those angles help define the shape of the figure, but BCE is formed by combining two specific segments shown in the diagram. The directly labeled angles 25° and 30° are what you need.

How do I know which angles to add together?

Look for angles that are adjacent (share a common ray) and together form the angle you're finding. In this case, BCF and FCE are next to each other and together make BCE.

What if the diagram shows different angle measures?

Always use the numbers shown in the diagram for your calculations. The angle measures given in the problem text (like 90° and 95°) provide context but may not be the ones you directly calculate with.

Can I solve this problem without the diagram?

No, the diagram is essential because it shows which specific angle segments combine to form BCE. Without seeing the geometric relationships, you can't determine the correct angle addition.

What does angle addition mean in geometry?

Angle addition means that when two angles share a common vertex and ray, their measures add up to form a larger angle. It's like: $\text{whole angle} = \text{part 1} + \text{part 2}$

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