How many degrees are in a triangle?
The three interior angles of any triangle on a flat surface always add up to 180 degrees, whatever the triangle's shape or size.
You can see why by drawing a line through one corner of a triangle, parallel to the opposite side. The three angles along that straight line match the three angles of the triangle, and a straight line measures 180 degrees. Another simple test is to tear off the three corners of a paper triangle and place them side by side: they form a straight line.
This rule helps find missing angles. If a triangle has angles of 50 and 60 degrees, the third must be 70 degrees. In an equilateral triangle, all three angles are equal, so each is 60 degrees. In a right triangle, one angle is 90 degrees, so the other two must add up to 90.
Curved surfaces are different
The 180-degree rule applies to flat, or Euclidean, geometry. On a curved surface like a sphere, a triangle's angles add up to more than 180 degrees. A triangle drawn from the North Pole down to the Equator and along it can have three right angles, adding up to 270 degrees.
Did You Know?
The exterior angles of any triangle, one at each corner, always add up to 360 degrees.