Five equal sides make up an equilateral pentagon. A rectangular pentagon's internal angles add up to 540 degrees. Since 360 ° + 180 ° = 540 °, each angle of a rectangular pentagon is 120 degrees.
The Pentagon is the world's most abundant rock element. It is a hard, siliceous sedimentary rock composed mainly of magnesium and calcium carbonates. The term "Pentagon" comes from the Greek word for five, which is used in reference to its shape.
Geographically, the Pentagon is one of the largest structures made by nature. It lies on the caprock of Arlington County, Virginia, near Washington, D.C. The caprock consists of layers of hard shale stacked over soft sandstone that was once part of a sea bed. The Pentagon itself is an anticlinal structure created as the North American continent drifted northward over 100 million years ago. An anticline is a mountain-like hill formed when horizontal layers of rock collapse downward into a valley.
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As a result, the total of a pentagon's internal angles is 540 degrees. All sides are the same length (congruent), as are all interior angles (congruent). Therefore, the pentagon is equilateral.
A pentagon is a 5-sided polygon. We may draw two diagonals from vertex A, dividing the pentagon into three triangles. To determine the sum of all the inside angles of a pentagon, multiply three times 180 degrees. The total is 540 degrees - 30 degrees per triangle minus three 90-degree angles. The measure of each angle in a pentagon is also 15 degrees.
There are many ways to find the measure of a single angle in a pentagon. Here's one method: Take the opposite side of the pentagon and extend it until it meets the other four sides. The five points of intersection form the center of a pentagram. The length of each side of the pentagram is equal to the distance between these points. Therefore, the measure of the angle at the center of the pentagram is also 15 degrees.
The pentagram center divides the pentagon into two congruent right triangles. Use the Pythagorean theorem to find the length of the fifth side of the pentagon. For example, if we want the length of side c, we can use c2 = a2 + b2. Now that we have the length of one side, we can easily find the remaining three lengths of the pentagon.
It's also possible to use trigonometry to find the measure of an angle in a pentagon.
Because all the angles of a regular pentagon, such as the one in your diagram, are the same, each internal angle is 540/5 = 108 degrees. Now consider the colored quadrilateral (ignore the colour and the common side shared by the triangle and pentagon). Because it is a four-sided form, the sum of its angles equals 360. In this case, the sum is easy to see because there are only two angles to add up: those of the pentagon and that of the colored quadrilateral. They sum to 180, so they must be equal.
Now look at the external angle of the colored quadrilateral. It's the opposite side of a pentagon, so it's also 108 degrees. The two angles are equal, so the two sides are equal too. Therefore, the area of the colored quadrilateral is the same as that of the pentagon.
Pentagrams are very important in many religions. For example, Christians believe that God created the world in six days and rested on the seventh. The Pentacle is one of the most important symbols in Christianity and has various meanings depending on the context. In mathematics, however, there is no connection between a pentagram and the number five. Instead, we can say that there is a connection between the pentagon and the number 108.