wikiHow Angle Calculator The calculation of angles usually depends on the properties and types of the angles. Here are the general steps to calculate the measure of an angle: 1. Identify the type of angle: The angle can be acute (less than 90 degrees), right (equal to 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (equal to 180 degrees), or reflex (greater than 180 degrees). 2. Determine the known angles: If there are any other known angles in the problem, make a note of them. 3. Apply the angle properties: Depending on the type of angle, there may be specific formulas or properties that can be used to calculate the measure of the angle. For example: * To find the measure of an angle in a right triangle, use the trigonometric ratios (sine, cosine, or tangent) involving the sides of the triangle. * To find the measure of an angle in a triangle, use the angle sum property (the sum of the angles in a triangle is 180 degrees). * To find the measure of an angle in a circle, use the fact that an inscribed angle is half the measure of the central angle that intercepts the same arc. 4. Use algebra to solve for the unknown angle: Once you have an equation involving the unknown angle, you can use algebra to isolate the variable and solve for its value. Here's an example of how to calculate the measure of an angle using the angle sum property of a triangle: Example: Find the measure of angle B in the triangle below, given that angle A measures 40 degrees and angle C measures 70 degrees. A / \ / \ / \ 10 / \ 8 / \ / \ / \ B ------------- C 12 Solution: Apply the angle sum property of triangles: the sum of the angles in a triangle is always 180 degrees. Add up the measures of angles A, B, and C: A + B + C = 180 40 + B + 70 = 180 Solve for the unknown angle, B: B = 180 - 40 - 70 B = 70 degrees Therefore, the measure of angle B in the triangle is 70 degrees. Page