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How to Calculate Angles: 9 Steps (with Pictures) – wikiHow


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Assistant Professor of Mathematics

This article was co-authored by Mario Banuelos, PhD and by wikiHow staff writer, Sophia Latorre. Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels. This article has been viewed 543,278 times.

Co-authors: 16

Updated: June 30, 2022

Views: 543,278

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To calculate the angles inside a polygon, first count the number of interior angles. A polygon has the same number of interior angles as sides. For example, a triangle always has 3 angles, while a square or rectangle always has 4, and so on. Next, use the formula (n – 2) x 180 to find the total number of degrees of all the interior angles combined. In this formula, n is equal to the number of interior angles. So, a triangle would have (3 – 2) x 180 degrees, or 180 degrees total. On the other hand, a quadrilateral, such as a square or a rectangle, would have (4 – 2) x 180 degrees, or a total of 360 degrees. If the polygon is regular—that is, if all the sides are the same length—then all you have to do is divide the total number of degrees of all the interior angles by the number of sides in the polygon. For instance, to calculate the angles in a regular pentagon, divide 540 degrees by 5 to get 108. Each angle in the pentagon is 108 degrees. If the polygon has irregular sides, your job is a little trickier. If you know all the angles in the polygon but one, you can add the known angles up and subtract the sum from the total number of degrees of all the interior angles. This will give you the number of degrees in the missing angle. In other cases, you may need to look up a formula or function that’s specific to the type of polygon you’re working with. For instance, you can use a sine, cosine, or tan function to find the angles in a right triangle depending on which angle you’re calculating and which side lengths you know. To find out how to calculate angle measure in a right triangle, read on!

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