Triangle Angles: Discover the 180° Rule
Understand that the interior angles of any triangle add to 180 degrees whatever its shape or size, and use that to find a missing angle and to classify triangles.
Before you try
What if you made a triangle very long and thin? Would the angles still add to 180?
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What happened?
Move a control to see what changes and why.
The 180 degree total holds for flat triangles. On a curved surface such as a globe, the three angles add up to more.
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Try these ideas
- Make a very flat triangle and check the angles still total 180.
- Turn on Put the three corners together and watch the straight line form.
- Switch to Find the missing angle and solve five problems.
Why it works
Take any triangle at all, tear off its three corners and lay them side by side. They always form a straight line, and a straight line is 180 degrees. That is the angle sum rule, and it holds for every triangle: tiny or huge, thin or fat, on any piece of flat paper. Because of it, knowing two angles is enough to work out the third by subtracting from 180.
Triangles also get names from their angles and their sides. A triangle with one 90 degree angle is right-angled, one with an angle over 90 is obtuse and one where all three are under 90 is acute. By sides they are equilateral, isosceles or scalene. In this simulator you move the three vertices, read each angle, and turn on a toggle that slides the three corner wedges together onto a straight line.
Check your understanding
Question 1 of 4
Two angles of a triangle are 55° and 65°. What is the third?
Do the angles of a very large triangle add to more than 180 degrees?
A triangle has an angle of 100°. What is it called?
Where is the largest angle in a triangle?
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
What will you discover next?
Try Pythagorean Theorem: Discover the Missing Side next.
For parents & teachers
- Cut out a paper triangle, tear the corners and line them up on a ruler.
- Ask whether a triangle could have two right angles, and why not.
- Measure the angles of a set square and add them up.