Find Angle CEB: Complex Geometry with 90°, 55°, and 95° Angles

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

Look for angles that share a common vertex and are adjacent (side by side). In this problem, angles CEB and CED both start at point E and together form the larger angle DEB.

Q: What does CEB + CED = DEB actually mean?

This means angle CEB and angle CED are adjacent angles that combine to make the total angle DEB. It's like adding two puzzle pieces to see the whole picture!

Q: How can I check if my answer makes sense?

Add your answer to the other known angle: $ 25° + 70° = 95° $. This should equal the given angle DEB, which is 95°. Perfect match!

Q: What if I can't see the angle clearly in the diagram?

Focus on the given information in the problem text rather than trying to measure angles visually. The key relationships and measurements are stated clearly in words.

Angle Addition with Given Measurements

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 CEB 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 angle C. E. B.

00:33 The whole angle B. E. D is the sum of its parts.

00:55 We'll put in the right values from what we are given, and solve for the angle.

01:10 Now, let's focus on angle C. E. B to find our answer.

01:17 And that's how we solve the problem!

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 CEB based on the data from the figure.

Step-by-step solution

Let's pay attention to the data in the question.

We know that angle DEB is equal to 95 degrees.

Let's break it down into an addition exercise:

$CEB+CED=DEB$

Now let's substitute the known data into the formula:

$CEB+70=95$

We'll move a term and keep the appropriate sign:

$CEB=95-70$

$CEB=25$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Angle Addition: Adjacent angles combine to form larger angles
Technique: Use CEB + CED = DEB to find CEB = 95 - 70 = 25°
Check: Verify 25° + 70° = 95° matches given angle DEB ✓

Common Mistakes

Avoid these frequent errors

Confusing angle measurements from the diagram
Don't use random angle values from different parts of the figure = wrong calculation! Many students grab any visible number instead of identifying which angles actually combine. Always identify the specific angles that form the relationship before calculating.

Practice Quiz

Test your knowledge with interactive questions

Find the measure of the angle $\alpha$

FAQ

Everything you need to know about this question

How do I know which angles add up together?

Look for angles that share a common vertex and are adjacent (side by side). In this problem, angles CEB and CED both start at point E and together form the larger angle DEB.

What does CEB + CED = DEB actually mean?

This means angle CEB and angle CED are adjacent angles that combine to make the total angle DEB. It's like adding two puzzle pieces to see the whole picture!

Why is angle CED equal to 70 degrees?

Look carefully at the diagram! The angle marked as 70° is positioned at point E between rays EC and ED, which defines angle CED.

How can I check if my answer makes sense?

Add your answer to the other known angle: $25° + 70° = 95°$ . This should equal the given angle DEB, which is 95°. Perfect match!

What if I can't see the angle clearly in the diagram?

Focus on the given information in the problem text rather than trying to measure angles visually. The key relationships and measurements are stated clearly in words.

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