Calculate Angle ABC: Geometry Problem with 70°, 18°, and 20° Angles

Q: Why do I add these three angles together?

These three angles are adjacent - they share vertex B and don't overlap. When adjacent angles are next to each other, they combine to form the total angle at that vertex.

Q: How can I tell if angles are adjacent?

Adjacent angles share a common vertex and have a common side between them, but don't overlap. In this diagram, all three angles meet at point B.

Q: Is this different from triangle angles?

Yes! Triangle interior angles sum to 180°, but these are adjacent angles at a single vertex. Don't confuse angle addition with triangle angle sums.

Q: What if the angles weren't adjacent?

If angles aren't adjacent, you cannot simply add them together. Always check that angles share a vertex and are positioned next to each other.

Angle Addition with Multiple Adjacent Angles

What is the size of angle ABC?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find angle ABC

00:03 The entire angle equals the sum of its parts

00:07 Let's sum its parts and solve to find the angle

00:10 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the size of angle ABC?

Step-by-step solution

In order to calculate the value of angle ABC, we will begin by calculating the sum of all the given angles.

That is:

$ABC=70+20+18$

$ABC=108$

Final Answer

108

Key Points to Remember

Essential concepts to master this topic

Rule: Adjacent angles at a vertex sum to create the whole angle
Technique: Add all given angles: 70° + 18° + 20° = 108°
Check: All three angles share vertex B and form angle ABC ✓

Common Mistakes

Avoid these frequent errors

Trying to use triangle angle sum theorem
Don't add angles to get 180° thinking it's a triangle = wrong concept! These are adjacent angles at point B, not triangle interior angles. Always identify if angles are adjacent at a vertex before adding them.

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 do I add these three angles together?

These three angles are adjacent - they share vertex B and don't overlap. When adjacent angles are next to each other, they combine to form the total angle at that vertex.

How can I tell if angles are adjacent?

Adjacent angles share a common vertex and have a common side between them, but don't overlap. In this diagram, all three angles meet at point B.

Is this different from triangle angles?

Yes! Triangle interior angles sum to 180°, but these are adjacent angles at a single vertex. Don't confuse angle addition with triangle angle sums.

What if the angles weren't adjacent?

If angles aren't adjacent, you cannot simply add them together. Always check that angles share a vertex and are positioned next to each other.

Could angle ABC be measured differently?

No - angle ABC specifically means the angle from ray BA to ray BC. The three given angles $70° + 18° + 20° = 108°$ make up this exact angle.

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