What is the sum of the inner angles of a pentagram? How many angles does a pentagram have?

The pentagram is a special decagonal shape, with 5 inner angles of 36 degrees and 5 of 252 degrees. (Note: finger shape, no line in it).

So the sum of the inner angles should be 1440 degrees.

Of course, if you only sum it, you can use the formula (n - 2) * 180 degrees to calculate.

For convex polygons, the proof of this formula is easy (as long as the interior is divided into some triangles), and for non-convex polygons such as the pentagram, the conclusion is also true, but the strict proof is not necessarily easy (it can still be divided into multiple triangles, but care must be taken to ensure that the triangle must be drawn).

To calculate the inner angles, the strict calculation method involves the nature of the pentagram, and the external regular pentagon of the pentagram can be considered to calculate.

However, there is a simple algorithm that can be used without requiring strict proofs:

Consider drawing a five-pointed star with a line inside in a row (starting from one corner, counting it is not difficult to see that the direction of movement of the line has turned 2 times, i.e. 720 degrees, and turned 5 times, so that each turn is 144 degrees. The acute inner angle of the pentagram complements the angle of rotation, so it is 180 - 144 = 36 degrees. And then the acute angle that is larger than 180 degrees is easy to calculate, slightly.

The pentagram has 5 inner angles and 5 outer angles. A five-pointed star is a type of star with five sharp corners drawn in five straight lines. The word "pentagram" comes from the Greek word and probably means "five straight lines" or "five lines".

Chinese meaning of "pentagram" is obvious, referring to a star with five horns, however, Chinese "pentagram" does not necessarily refer to a "standard" pentagram Chinese the term "pentagram" sometimes refers to all stars with five horns.

Pentagram for daily useThere are many countries whose flag designs include a five-pointed star: Ethiopia, Morocco, Vietnam, North Korea, the People's Republic of China, the United States, and many more. Many times, the middle of the pentagram is filled, removing the demarcation between the pentagram and the five isosceles triangles.

The inner angle of the pentagram and the calculation method are as follows:

The middle part of the pentagram is a regular pentagon, and the sum formula of the inner angles of the n-sided is (n-2)180 degrees, so each inner angle of the regular pentagonal is (5-2)*180 5=108 degrees, look at the triangle with thick lines, this is an isosceles triangle, so the degree of each angle of the pentagram is (180-108) 2 = 36 degrees, and the sum of the degrees of the five angles is 36*5=180 degrees.

First of all, you need to grasp the concept of the outer angle of a triangle. One diplomacy of a triangle is equal to the sum of two interior angles that are not adjacent to it. In the pentagram, you might as well draw it with a pen.

Then observe one of the small triangles (one of the five corners), the two inner angles near the center are one outer angle corresponding to the two triangles of the first spring, and the remaining one small corner reduces the five corners to one triangle. So the sum of the inner angles of the pentagram is 180 degrees.

Characteristics of internal angles: In mathematics, the sum of the internal angles of a triangle is 180°, and the sum of the internal angles of a quadrilateral (polygon) is 360°. And so on, add one side to the nain, and add 180 degrees to the sum of the inner angles.

The sum of the internal angles is: (n 2) 180° The number of internal angles of a regular polygon is: (n 2) 180° n For example, the inner angles of a triangle and the inner angles of a triangle are the sum of the three angles inside a triangle, and an inner angle is any one of the corners.

The sum of the inner angles of the pentagram is 900°.

A regular pentagram can be divided into 5 congruent triangles and a regular pentagon.

And all 5 congruent triangles are isosceles triangles.

It can be seen that the sum of the inner angles of the five triangles is 180 degrees*5=900 degrees;

According to the 5-sided inner angle is 108 degrees.

180 degrees -108 degrees to 72 degrees. That is, the base angle of 5 congruent triangles is 72 degrees.

72*10 (10 bottom corners) = 720 degrees. 900-720 = 180 degrees. Each angle is 36 degrees.

The sum of the inner angles of the pentagram is 180 degrees.

The specific solution ideas are as follows:

In the figure below, for example, the five points form a regular pentagon. Each corner of a regular pentagon is 108°, so the angle with 7 as the vertex is also 108°. Then because the sum of the inner angles of the isosceles triangle is 180°, the other two angles are (180°-108°) 2=36°.

Then the sum of the inner angles of the pentagram = 36° 5 = 180°.

The algorithm of the sum of the inner angles of the pentagram is: according to the formula of finding the sum of the inner angles of the pentagram, the pentagram n=10(10-2)*180°=1440°. First of all, find a five-pointed star of any shape, long, short, wide, flat.

And each outer corner is marked with a serial number.

In addition to this, there are:

Then take the first horn and start looking. What we've all learned before is that the sum of the inner angles of a triangle = 180 degrees, and that the outer angles of one corner are equal to the sum of two non-adjacent inner angles.

According to the above Li Min orange celery theory, it can be deduced that e+b=m, and Hashibi sees EGC as a triangle, a, b are the inner angles, and m is the outer angle.

In the same way, the same theory is obtained by looking at the other angles as large triangles in turn.

The outer angle of the EGC is H, and the outer angle of the FDB is H, so that the angle GB is made. The angle ghb is a triangle with an inner sum of 180 degrees. So the sum of the inner angles of all five corners of the triangle is 1440 degrees.

The pentagram is a decagonal shape, and the five raised vertex angles, which are usually what we call the pentagram, form a shining five-pointed star. Five recessed corners. The sum of the inner angles of the polygon is (n-2) 180 degrees. So the sum of the inner angles of the pentagram is equal to 1440 degrees.

Connect the center point of the pentagram with the vertices of the five corners of the center of the pentagram, and then connect the concave vertices to the center. Ten congruent triangles are formed, and the sum of the inner angles of the ten triangles is equal to 1800 degrees, minus the middle circumference angle of 360 degrees. It is also proved that the sum of the inner angles of the pentagram is equal to 1440 degrees.

The sum of the internal angles of the pentagon = (5-2) 180° = 540°, the number of one internal angle of the regular pentagon = 540° 5 = 108°, the pentagram is a standard figure, the five angles are equal, and the diagram forms an isosceles triangle with a vertex angle of 108°, 3 = 5 = (180°-108°) 2 = 36°

Answer: The sum of the inner angles of a pentagram is 180° (5 angles protruding from one finger).

The pentagram has 5 inner angles and 5 outer angles. The inner angle is acute, and the degree is 36°; The outer angle is obtuse and the degree is 108°.

A five-pointed star is a star with five sharp corners drawn in five straight lines. English"Pentagram"The word (pentagram) comes from the Greek word and probably meant it"Five straight lines"or"Five lines"。Chinese"Pentagram"The meaning is obvious, the history refers to the shape of a star with five horns.

However, Chinese"Pentagram"Not necessarily meant"standards"The five-pointed star limb is auspicious. Chinese"Pentagram"The term is sometimes used to refer to all stars with five horns.