An equilateral triangle has three equal interior angles and we know their total is 180 degrees, so divide 180 by 3 and the answer is 60 degrees.
An isosceles triangle has two equal angles. Add these angles together and subtract the total from 180 to find the third angle. If you are given the third angle, subtract it from 180 and divide your answer. For example, if you are told that the third angle is 32 degrees, subtract 32 from 180. Take the result, in this case 148, and divide it by two. The two equal angles are each 72 degrees.
You have to know two of the angle measures for a scalene triangle to find the third. Add these two measures and subtract the result from 180. For example, if you are told that two of the angles are 45 degrees and 55 degrees, add 45 to 55. The result is 100. Subtract 100 from 180 and you find that the third angle measure is 80 degrees.
Use a protractor if you don't know the measures of any of the angles. Place the protractor's origin (small hole) over the vertex of the angle to be measured. Align the protractor's baseline along one of the angle's legs. Read the angle measure off the appropriate scale.
To find the side lengths of a triangle, first determine if it is an equilateral triangle. If it is and you know one of the side lengths, the other two side lengths are the same.
If you are dealing with a right triangle (one with a 90 degree angle), you can use the Pythagorean Theorem to find the measure of an unknown side. The Pythagorean Theorem states
a^2 + b^2 = c^2,
where c is the side length opposite the 90 degree angle (the hypotenuse) and a and b are the other two sides. Therefore, if you know two side lengths, you can plug them into the equation and solve for the unknown measure.
If you are not dealing with a right triangle, you can use the Law of Sines to find the missing measures. The Law of Sines states that, "The sides of a triangle are to one another in the same ratio as the sines of their opposite angles." When you use the Law of Sines, you are actually venturing into trigonometry, not geometry. The Law of Sines can also be expressed as
sin(A)/a = sin(B)/b = sin(C)/c, or
a/sin(A) =b/sin(B) = c/sin(C),
where A is the angle across from side a, B is the angle across from side b and C is the angle across from side C. Use these ratios to solve for whatever side you are missing by cross multiplying.