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This article was co-authored by Jake Adams. Jake Adams is an academic tutor and owner of an online tutoring business in Santa Monica, California that provides study resources and online tutors for academics, K-College, SAT & ACT preparation, and college admissions applications. With over 14 years of professional teaching experience, Jake is committed to providing his clients with the best online teaching experience and the best undergraduate and postgraduate tutors from colleges across the country. Jake holds a BS in International Business and Marketing from Pepperdine University.
How Many Sides Does A Polygon Have
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How Many Sides Does A Regular Polygon Have If One Of It’s Interior Angles Measure 162?
Finding diagonals in polygons is an important skill to develop in mathematics. It may seem difficult at first, but once you learn the basic formula, it’s really easy. A diagonal is any line segment drawn between the vertices of a polygon that does not include the sides of the polygon.
A polygon is any shape that has more than three sides. Using a very simple formula, you can calculate the number of diagonals in any polygon with 4 sides or 4,000 sides.
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This article was co-authored by Jake Adams. Jake Adams is an academic tutor and owner of an online tutoring business in Santa Monica, California that provides study resources and online tutors for academics, K-College, SAT & ACT preparation, and college admissions applications. With over 14 years of professional teaching experience, Jake is committed to providing his clients with the best online teaching experience and the best undergraduate and postgraduate tutors from colleges across the country. Jake holds a BS in International Business and Marketing from Pepperdine University. This article has been viewed 343,222 times.
Polygons And Symmetry Lesson 1
To find out how many diagonals a polygon has, first count the number of sides or straight lines that make up the polygon. Then subtract 3 from the sides. Next, multiply that number by the side number. Finally, divide the answer by 2 and you will get the number of diagonals in the polygon. For example, if a polygon has 6 sides, it has 9 diagonals. For an alternative way of finding the number of diagonals in a polygon, read on! I am a former math teacher and owner of DoingMaths. I love writing about math, its applications, and fun math facts.
A polygon is any 2D shape that consists of certain straight lines. For example; A triangle is a three-sided polygon, a square is a four-sided polygon, etc.
All of these polygons have inner and outer angles, but how many are these angles? Are they always the same? Is there a pattern to their overall case? Let’s start by looking at the angles in the triangle.
The interior angle of a polygon, as the name suggests, is the interior angle formed at the point where the edges of the polygon meet.
What Do The Angles In A Polygon Add Up To?
Before we start looking at the interior angles of polygons, let’s start with a three-sided polygon, otherwise known as a triangle.
By considering a triangle with an additional straight line parallel to the base of the triangle as shown in the diagram below, we can quickly find the sum of the three interior angles.
To find the sum of the angles in a + b + c we note that the angle formed between the triangle and the top line of the parallelogram is the inverse of b, so b = x. Likewise, c = y. We also see that x, a, and y intersect on a straight line, so a + x + y = 180°.
A four-sided polygon is known as a quadrilateral. This group includes squares, rectangles, parallelograms and other familiar shapes.
How Many Sides Does A Regular Polygon Have If The Measure Of An Exterior Angle Is 24^@?
Now, when the angles in a triangle add up to 180°, we can quickly calculate the sum of the angles in a rectangle.
See the diagram below. We take a rectangle and divide it diagonally into two triangles. From the diagram we can understand that the interior angles of two triangles are the quadrilateral angles of four quadrilaterals. Therefore, the measure of the angle of the rectangle must be twice the angle of the triangle.
We can use the same method to calculate the angles in a polygon with more than four sides. Simply cut the polygon into triangles using diagonal lines, making sure all the corners in the triangle match the corners in the polygon. Then multiply the number of triangles by 180° to get the sum of the interior angles of the polygon.
On the pentagon diagram we can see that the pentagon is divided into three inner triangles and the sum of the interior angles should be 3 × 180° = 540°.
How Many Sides Does A Regular Polygon Have If Each Of Its Interior Angles Is 165 ^∘ ?
It can be seen from our example that the number of triangles dividing the polygon is two less than the total number of sides. For example, a quadrilateral is divided into 4 – 2 = 2 triangles and a pentagon is divided into 5 – 2 = 3 triangles.
You can quickly verify that this can be expanded to include more polygons. Regardless of the number of sides, we subtract two to give the number of triangles by which we divide the polygon. Multiplying this triangular number by 180°, we get the sum of the interior angles.
Since we always divide a polygon into two triangles that have fewer sides, a polygon with n sides can be divided into n – 2 triangles such that the sum of the interior angles is 180(n – 2)°.
So far we’ve looked at the inner corners of the polygon, but what about the outer corners?
How Many Sides Does A Square Have?
The outer corner is drawn on the outside of the polygon and formed by extending the side and measuring the angle between the drawn side and the next side. This is shown in the diagram below.
If an exterior angle is formed by a straight line, the corresponding exterior and interior angles must always add up to 180°.
To calculate the sum of the outer corners, imagine you have a large polygon on the floor and you walk on one side. When you reach a corner, you must rotate the outer corner to face the next side. You go on this second side and when you reach the corner, drive around the next outer corner to continue your journey.
This goes on around every corner until you get back to your starting point. At this point, you will now face the direction you started with the full turn. A full circle is 360°, so all exterior angles must add up to 360°.
Solution: How Many Sides Are In A Polygon If Each Interior Angle Is 165°
This is the same no matter how many sides the polygon has. The exterior angles of a triangle add up to 360°; The external angles of the decagon are 360°.
This content is accurate and correct to the best of the author’s knowledge and is not intended to replace the formal and personal advice of a qualified professional.
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