Calculate Triangle Angle ABC: Given 60° and 50° Angles

Q: How do I know if an angle is interior or exterior?

An interior angle is inside the triangle between two sides. An exterior angle is outside the triangle, formed by extending one side. In this diagram, ABC is exterior because it's outside the triangle.

Q: Why don't I use the 180° triangle rule here?

The 180° rule applies to the three interior angles of a triangle. Since ABC is an exterior angle, we use the exterior angle theorem instead: exterior angle = sum of two remote interior angles.

Q: What are 'remote interior angles'?

Remote interior angles are the two interior angles that don't share a vertex with the exterior angle. For exterior angle ABC, the remote angles are the 60° and 50° angles.

Triangle Angle Sum with Exterior 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

00:12 Let's sum up the known angle parts and solve to find the angle

00:22 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

What is the size of angle ABC?

Step-by-step solution

In order to calculate the value of angle ABC, we must calculate the sum of all the given angles.

That is:

$ABC=60+50$

$ABC=110$

Final Answer

110

Key Points to Remember

Essential concepts to master this topic

Rule: Exterior angle equals sum of two non-adjacent interior angles
Technique: Add the two remote angles: $60° + 50° = 110°$
Check: Interior angle ABC + exterior angle = 180°: 70° + 110° = 180° ✓

Common Mistakes

Avoid these frequent errors

Using triangle angle sum theorem incorrectly
Don't add all three angles thinking ABC + 60° + 50° = 180°! This treats ABC as an interior angle when it's actually exterior. Always identify if the angle is interior (inside triangle) or exterior (outside triangle) first.

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 if an angle is interior or exterior?

An interior angle is inside the triangle between two sides. An exterior angle is outside the triangle, formed by extending one side. In this diagram, ABC is exterior because it's outside the triangle.

Why don't I use the 180° triangle rule here?

The 180° rule applies to the three interior angles of a triangle. Since ABC is an exterior angle, we use the exterior angle theorem instead: exterior angle = sum of two remote interior angles.

What are 'remote interior angles'?

Remote interior angles are the two interior angles that don't share a vertex with the exterior angle. For exterior angle ABC, the remote angles are the 60° and 50° angles.

Can I check my answer another way?

Yes! The exterior angle ABC and its adjacent interior angle must add to 180° (straight line). So if ABC = 110°, then the adjacent interior angle = 70°, and 70° + 60° + 50° = 180° ✓

What if I calculated ABC as an interior angle by mistake?

If you used 60° + 50° + ABC = 180°, you'd get ABC = 70°. This would be the interior angle adjacent to the exterior angle ABC. The actual exterior angle ABC = 180° - 70° = 110°.

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