Pre-Algebra
Geometry
Interior and exterior angles of triangles
20 practice questions
0 video lessons
Theory + worked examples
Interior and Exterior Angles of Triangles
California Pre-Algebra • Standard 8.G.5 • Geometry
Interior and Exterior Angles of Triangles is a topic in Geometry in the California Common Core State Standards. It is aligned to Standard 8.G.5, which requires students to use the angle sum and exterior angle relationships of triangles.
A triangle's interior angles sum to \(180^\circ\), and an exterior angle equals the sum of the two remote interior angles.
Theory
The interior angles of a triangle sum to \(180^\circ\).
An exterior angle equals the sum of the two remote interior angles.
Interior angles sum to \(180^\circ\).
Triangle angle facts.
Angle sum:
\[a+b+c=180^\circ\]
Exterior angle = sum of remote interiors.
How to find a triangle's angle
- Add the known interior angles.
- Subtract from \(180^\circ\) for the third.
- For an exterior angle, add the remote interiors.
- Set up an equation for unknowns.
Example 1 — Third angle
Two angles are \(50^\circ\) and \(60^\circ\). Find the third.
Solution
They sum to \(180\).
| \(180-50-60\) | \(=\) | \(70^\circ\) |
Example 2 — Exterior angle
An exterior angle equals two remote interiors \(40^\circ\) and \(65^\circ\).
Solution
Add them.
| \(40+65\) | \(=\) | \(105^\circ\) |
Example 3 — Equilateral
Each angle of an equilateral triangle is?
Solution
Divide \(180\) by \(3\).
| \(\dfrac{180}{3}\) | \(=\) | \(60^\circ\) |
Example 4 — Solve
Angles \(x, x, 2x\) form a triangle. Find \(x\).
Solution
Sum to \(180\).
| \(4x\) | \(=\) | \(180\) |
| \(x\) | \(=\) | \(45^\circ\) |
Common pitfalls
Interior angles sum to \(180\), not \(360\).
An exterior angle uses the two remote interiors.
Each equilateral angle is \(60^\circ\).
Frequently asked questions
What do a triangle's angles sum to?
\(180^\circ\).
What is an exterior angle equal to?
The sum of the two remote interior angles.
What is each angle of an equilateral triangle?
\(60^\circ\).
Third angle if two are \(50^\circ,60^\circ\)?
\(70^\circ\).
← Previous subtopic
Transversals of parallel lines
Next subtopic →
Scale drawings and geometric figures
More in Geometry