Three straight lines intersect at one point, how many pairs of vertex angles are there? How many pai

Three straight lines intersect at one point, how many pairs of vertex angles are there? How many pairs of proximal complements are there?

Solution: Two straight lines intersect at a point with 2 pairs of vertex angles, there are 2 pairs of adjacent complementary angles, and three straight lines intersect at one point, which can be regarded as "three two straight lines intersect at one point".

Three straight lines intersect at a point, there are 3 2 = 6 pairs of vertex angles; There are 6 pairs of adjacent complementary angles;

Four straight lines.

Solution: Two straight lines intersect at one point with two pairs of vertex angles, and four straight lines intersect at one point can be seen as "four two straight lines intersect at one point".

Four straight lines intersect at one point, there are 4 2 = 8 pairs of vertex angles; There are 8 pairs of adjacent complement angles;

What about n straight lines?

Solution: There are 2 pairs of vertex angles where two straight lines intersect at a point, and the intersection of n straight lines at a point can be regarded as "n two straight lines intersect at a point".

n straight lines intersect at a point, and there are n(n-1) pairs of vertex angles; There is n(n-1) pair of adjacent complement angles.

Two straight lines intersect with 1 intersection point, 2 pairs of vertex angles and 4 pairs of adjacent complementary angles.

Add a line and you will have 2 more intersections, add another line and you will have 3 more intersections, and add another line and you will have 4 more intersections,.。

Therefore. n straight lines intersect in pairs, and 1+2+ can be obtained. n-2)+(n-1)=n(n-1) 2 intersections.

n(n-1) pairs of vertex angles and 2n(n-1) pairs of adjacent complementary angles.

At n = 4, 12 pairs of apical angles.

24 pairs of adjacent complementary angles.

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n straight lines intersect with n(n-1) pairsto the apex corners2n(n-1) pairAdjacent complement anglesIt can also be said as: any two straight lines intersect and there will be 2 pairs of vertex angles and 4 pairs of adjacent complementary angles; The intersection of three straight lines has 6 pairs of vertex angles and 12 pairs of adjacent complementary angles. Four straight lines intersect to produce 12 pairs of vertex angles and 24 pairs of adjacent complementary angles; The five lines have a total of 20 pairs of vertex angles and 40 pairs of adjacent complementary angles.

Conditions for the intersection of straight lines:If two lines have only one common point, they are said to intersect. Within the same plane, the positional relationship of two straight lines:

Intersecting, parallel. Two straight lines with a unique common point are called intersecting lines.

It has an infinite number of axes of symmetry.

One of them is itself, and all the straight lines (there are innumerable) axes of symmetry perpendicular to it. There is only one straight line at the two points on the plane that do not coincide, that is, the two points that do not coincide determine a straight line. On the spherical surface, two points of the game can be played in countless similar straight lines.

4 straight lines intersect, there are 4 (4-1) pairs of apex angles and 8 (4-1) pairs of adjacent complementary anglesIt can also be said that any two straight lines intersect must have 2 pairs of vertex angles and 4 pairs of adjacent complementary angles; The intersection of three straight lines has 6 pairs of vertex angles and 12 pairs of adjacent complementary angles. Four straight lines intersect to appear 12 pairs of vertex angles, and 24 pairs of neighbors complement and merge early angles; The five lines have a total of 20 pairs of vertex angles and 40 pairs of adjacent complementary angles.

Intersecting Condition:If two lines have only one common point, they are said to intersect. Within the same plane, the positional relationship of two straight lines:

Intersecting, parallel. Two lines with a single common point are called intersecting lines.

It has an infinite number of axes of symmetry, one of which is itself, and all the straight lines (with an infinite number of axes) perpendicular to it. If there is only one straight line at two points that do not coincide on the plane, that is, two points that do not coincide determine a straight line. On a spherical surface, crossing two points can make an infinite number of similar straight lines.

n straight lines intersect, the number of vertex angles = the number of intersection points * 2;Number of adjacent complement angles = number of intersection points * 4,In this problem, we should first consider that if there are only two straight lines, and the two lines are not parallel, then there will be an intersection point, 2 pairs of vertex angles and 4 pairs of adjacent complementary angles.

Cases where there are multiple straight lines:

Draw the 3rd straight line, as long as it is not parallel to the first 2, it will intersect with the first 2 straight lines, add 2 intersections, and 1+2 intersections will be added to the total number of points. Draw the 4th straight line, as long as it is not parallel to the first 3, it will intersect with the first 3 straight lines, adding 3 intersections, a total of 1+2+3 intersections. Draw the 5th straight line, as long as it is not parallel to the first 4, it will intersect with the first 4 straight lines, adding 4 intersections, a total of 1+2+3+4 intersections.

Draw the nth straight line, as long as it is not parallel to the previous n-1, it will intersect with n-1 straight macro lines, adding n-1 intersections, a total of 1+2+3+4+n-1 intersections.

Therefore, n straight lines that are not parallel to each other, the number of intersecting points = 1 + 2 + ...n-1) = n(n-1) 2.

The 4 straight lines intersect with 12 pairs of fast-pin apex. n straight lines intersect with mu search n(n-1) pairs of opposite top angles, 4 straight lines intersect with 24 pairs of adjacent complementary angles, n straight lines intersect with missing rows, n[2(n-1)] pair of adjacent complementary angles.

That is, Wang stupidly looked at how many pairs of straight lines, each pair of straight lines had two pairs of top corner socks, and four pairs of adjacent gear slippery corners.

n（n-1）

2n（n-1）

Hello. Four straight lines intersect with a maximum of six intersections.

Each intersection has two pairs of vertex angles, with a maximum of 12 pairs of vertex angles.

Each intersection has four sets of complement angles, up to a maximum of 24 sets of complement angles.

Good luck and goodbye.

n straight lines intersect at a point and there are several pairs of pairs of adjacent complementary angles: every two lines form two pairs of vertex angles.

So there are c(n,2)*2=n*(n-1) pairs of vertex angles, and each of the two straight lines forms four pairs of adjacent complementary angles.

So there is c(n,2)*4=2n*(n-1) pair of adjacent complement angles.