How to Calculate Angles
Count the number of sides in the polygon., Find the total measure of all angles in the polygon., Determine if the polygon is a regular polygon., Add the measures of the known angles of the polygon together, then subtract it from the total angle...
Step-by-Step Guide
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Step 1: Count the number of sides in the polygon.
The formula for finding the total measure of all interior angles in a polygon is (‘’n’’ – 2) x 180, where ‘’n’’ is the number of sides, as well as the number of angles, the polygon has.Some common polygon total angle measures are as follows:
The angles in a triangle (a 3-sided polygon) total 180 degrees.
The angles in a quadrilateral (a 4-sided polygon) total 360 degrees.
The angles in a pentagon (a 5-sided polygon) total 540 degrees.
The angles in a hexagon (a 6-sided polygon) total 720 degrees.
The angles in an octagon (an 8-sided polygon) total 1080 degrees. , A regular polygon is a polygon whose sides are all the same length and whose angles all have the same measure.
Equilateral triangles and squares are examples of regular polygons, while the Pentagon in Washington DC is an example of a regular pentagon and a stop sign is an example of a regular octagon.
If the polygon is a regular polygon, simply divide the total measure of all its angles by the number of its angles.Thus, the measure of each angle in an equilateral triangle is 180/3, or 60 degrees, and the measure of each angle in a square is 360/4, or 90 degrees. (Although a rectangle is not a regular polygon, by definition, all its angles are also right angles, measuring 90 degrees each.) If the polygon is not a regular polygon, you need to know the measures of the other angles in the polygon to calculate the measure of an unknown angle.
Proceed to the next step. , Most geometry problems of this nature work with triangles or quadrilaterals, because there are fewer numbers to work with, so we’ll do likewise.
If two of the angles of a triangle have measures of 60 and 80 degrees, add the numbers together to get a sum of
140.
Then, subtract this sum from the total angle measure for a triangle, which is 180 degrees: 180 – 140 = 40 degrees. (This kind of triangle, where all the angles have different measures, is called a scalene triangle.) You can write the above method out as a formula: ‘’a’’ = 180 – (‘’b’’ + ‘’c’’), where ‘’a’’ is the angle whose measure you’re trying to find, and ‘’b’’ and ‘’c’’ are the angles whose measures you already know.
For polygons with more than 3 sides, simply replace “180” with the total angle measure of the polygon and add another term for each additional known angle.
Some polygons offer “cheats” to help you figure out the measure of the unknown angle.
An isosceles triangle is a triangle with two sides of equal length and two angles of equal measure.
A parallelogram is a quadrilateral with opposite sides of equal lengths and angles diagonally opposite each other of equal measure. -
Step 2: Find the total measure of all angles in the polygon.
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Step 3: Determine if the polygon is a regular polygon.
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Step 4: Add the measures of the known angles of the polygon together
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Step 5: then subtract it from the total angle measure of the polygon.
Detailed Guide
The formula for finding the total measure of all interior angles in a polygon is (‘’n’’ – 2) x 180, where ‘’n’’ is the number of sides, as well as the number of angles, the polygon has.Some common polygon total angle measures are as follows:
The angles in a triangle (a 3-sided polygon) total 180 degrees.
The angles in a quadrilateral (a 4-sided polygon) total 360 degrees.
The angles in a pentagon (a 5-sided polygon) total 540 degrees.
The angles in a hexagon (a 6-sided polygon) total 720 degrees.
The angles in an octagon (an 8-sided polygon) total 1080 degrees. , A regular polygon is a polygon whose sides are all the same length and whose angles all have the same measure.
Equilateral triangles and squares are examples of regular polygons, while the Pentagon in Washington DC is an example of a regular pentagon and a stop sign is an example of a regular octagon.
If the polygon is a regular polygon, simply divide the total measure of all its angles by the number of its angles.Thus, the measure of each angle in an equilateral triangle is 180/3, or 60 degrees, and the measure of each angle in a square is 360/4, or 90 degrees. (Although a rectangle is not a regular polygon, by definition, all its angles are also right angles, measuring 90 degrees each.) If the polygon is not a regular polygon, you need to know the measures of the other angles in the polygon to calculate the measure of an unknown angle.
Proceed to the next step. , Most geometry problems of this nature work with triangles or quadrilaterals, because there are fewer numbers to work with, so we’ll do likewise.
If two of the angles of a triangle have measures of 60 and 80 degrees, add the numbers together to get a sum of
140.
Then, subtract this sum from the total angle measure for a triangle, which is 180 degrees: 180 – 140 = 40 degrees. (This kind of triangle, where all the angles have different measures, is called a scalene triangle.) You can write the above method out as a formula: ‘’a’’ = 180 – (‘’b’’ + ‘’c’’), where ‘’a’’ is the angle whose measure you’re trying to find, and ‘’b’’ and ‘’c’’ are the angles whose measures you already know.
For polygons with more than 3 sides, simply replace “180” with the total angle measure of the polygon and add another term for each additional known angle.
Some polygons offer “cheats” to help you figure out the measure of the unknown angle.
An isosceles triangle is a triangle with two sides of equal length and two angles of equal measure.
A parallelogram is a quadrilateral with opposite sides of equal lengths and angles diagonally opposite each other of equal measure.
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