How this instrument works
Every corner of a triangle has both an interior angle (the figure measured inside the triangle itself) and, once one side is extended straight past that corner, an exterior angle sitting right alongside it. Because the interior value and the extended straight line together always form a straight angle of exactly 180°, the exterior figure is simply whatever remains: exterior = 180° − interior.
This relationship holds at every corner of every triangle without exception, since it comes directly from the definition of a straight line rather than from anything specific to triangles — the two figures at any single vertex are what's called a linear pair, and linear pairs always sum to 180° regardless of the surrounding shape.
There's a second, equally useful fact worth knowing alongside this one: the Exterior Angle Theorem states that any exterior measure equals the SUM of the two interior figures that aren't adjacent to it. Both facts describe the same quantity from different directions — one from the adjacent corner alone, the other from the two remote ones — and both always agree.
- Enter the triangle's interior angle at the corner you're interested in into the Interior angle field.
- Read Exterior angle: the sheet subtracts your entry from 180° directly.
- Repeat for each of the triangle's three corners to find all three exterior figures in turn.
Worked example — an interior angle of 70°
A triangle's interior angle at one corner is 70°. Extending one side straight past that corner creates an exterior figure of 180° − 70° = 110° — the two values together always fill out a full straight line at that vertex.
A right interior corner of exactly 90° gives an exterior figure of exactly 90° too — the one special case where the two coincide, since both must be precisely half of 180°. An obtuse interior measure of 120°, by contrast, gives a much smaller exterior value of only 60°, shrinking as the interior one grows.
Questions
How do you find a triangle's exterior angle?
Subtract the interior value from 180°: exterior = 180° − interior. This works because the interior figure and its adjacent exterior partner always sit together on a straight line, and any straight line's measure is exactly 180°.
Why do the two always sum to 180°?
Because extending one side of a triangle past a corner creates a straight line through that corner, and a straight line's measure is, by definition, always exactly 180° — the interior figure and the newly formed exterior one are simply the two pieces that line splits into.
What is the Exterior Angle Theorem?
It states that any exterior measure of a triangle equals the SUM of the two interior figures that are NOT adjacent to it (the two 'remote' corners). This gives a second, independent way to find the same value this calculator computes directly.
Can the exterior figure exceed 180°?
Not defined this standard way — since a triangle's interior corner is always between 0° and 180°, the corresponding exterior value (180° minus that corner) is also always between 0° and 180°.
Does every corner of a triangle have its own exterior partner?
Yes — each of the three corners has its own interior-exterior pair, computed the same way. A triangle's three exterior figures, one per corner, always sum to exactly 360°, a full turn, regardless of the triangle's shape.