In geometry, an angle is a space between 2 rays (or line segments) with the same endpoint (or vertex). The most common way to measure angles is in degrees, with a full circle measuring 360 degrees. You can calculate the measure of an angle in a polygon if you know the shape of the polygon and the measure of its other angles or, in the case of a right triangle, if you know the measures of two of its sides. Additionally, you can measure angles using a protractor or calculate an angle without a protractor using a graphing calculator. This is to allow you to calculate angles
Calculating Interior Angles in a Polygon
- For instance, a triangle has 3 sides and 3 interior angles while a square has 4 sides and 4 interior angles.
- Equilateral triangles and squares are examples of regular polygons, while the Pentagon in Washington, D.C. is an example of a regular pentagon and a stop sign is an example of a regular octagon.
- For example, if you know that 4 of the angles in a pentagon measure 80, 100, 120, and 140 degrees, add the numbers together to get a sum of 440. Then, subtract this sum from the total angle measure for a pentagon, which is 540 degrees: 540 – 440 = 100 degrees. So, the missing angle is 100 degrees.
Tip: Some polygons offer “cheats” to help you figure out the measure of the unknown angle. An isosceles triangle is a triangle with 2 sides of equal length and 2 angles of equal measure. A parallelogram is a quadrilateral with opposite sides of equal lengths and angles diagonally opposite each other of equal measure.
Finding Angles in a Right Triangle
Tip: You can use a graphing calculator to solve your equations or find a table online that lists the values for various sine, cosine, and tangent functions.
- If you have a graphing calculator, simply type 0.5 and press sine-1. If you don't have a graphing calculator, use an online chart to find the value. Both will show that x = 30 degrees.
- Plug 0.833 into your graphing calculator and press cosine-1. Alternatively, look up the value in a cosine chart. The answer is 33.6 degrees.
- Find the value in a tangent chart or press 0.75 on your graphing calculator, then tangent-1. This is equal to 36.9 degrees. There are some methods to Calculate Angles.