-
This question may seem simple, but it actually involves the combination of angles and mathematical induction.
First of all, we can consider that the minimum angle that can be drawn by a triangular ruler is 15 degrees, and the maximum angle is 180 degrees.
The smallest angle that a triangular ruler can draw is 15 degrees.
The maximum angle that can be drawn with a triangular ruler is 180 degrees.
The types of angles that can be drawn with a triangular ruler depend on several factors:
1.the scale of the triangular ruler itself;
2.angular combinations between triangular rulers;
3.Multiples of angles.
Next, we can consider using mathematical induction to prove:
For any n, the triangular ruler can draw an n-fold angle of 15 up to 180 degrees.
When n=1, it is clearly true.
Suppose that when n = k, that is, the triangular ruler can draw a k-fold angle of 15 up to 180 degrees.
Then when n=k+1, the angle range that can be drawn by the triangular ruler is:
15 + 15k + 15(k+1) < = 180 Simplification: 15k + 15 + 15 < = 180 Shift: 15k < = 180 - 15 - 15 - 15 Simplification: 15k < = 150
So k < = 12-1
Obviously, this is also true when n=k+1.
So for any n, the triangular ruler can draw an angle of 15 times n, up to 180 degrees.
So, the triangular ruler can draw 11 different angles.
-
The angles of the triangle are 45 degrees, 45 degrees, and 90 degrees; 30 degrees, 60 degrees, 90 degrees can be spelled out with a pair of triangles to spell out 12 different angles. With a triangle, you can spell out 30 + 90 = 120 degrees, 60 + 90 = 150 degrees, 30 + 45 = 75 degrees, 60 + 45 = 105 degrees, 90 + 90 = 180 degrees, 90 + 45 = 135 degrees.
-
1. First of all, a ° is drawn from an angle.
2. The second is the ° of the combination of the two angles (15=45-30, 75=45+30, 105=45+60, 120=60+60, 135=45+90, 150=60+90).
3. Again, it is a combination of three angles: 165° (165 = 30 + 45 + 90).
4. Don't use the last corner, draw a straight line, that is, a flat angle: 180°.
-
Since the degrees of each angle in a pair of triangles are °, the angles that can be obtained by combining them are: 60°-45°=15°, 60°+45°=105°, 60°+90°=150°, 90°+45°=135°, 90°+30°=120°, 30°+45°=75°.
Explanation of terms: The multi-functional triangular ruler is a circle drawing mechanism composed of a rotating ring and a turntable at the two acute angles of the original triangular ruler, a pendulum needle-shaped angle drawing mechanism is installed at the protractor, a frame is installed at the bottom edge, and a groove rail is provided in the frame, and a parallel line drawing mechanism composed of a positioning mechanism composed of a schedule plate, an elastic material and a slider embedded in the groove is installed in the groove to facilitate sliding.
It maintains the function of the original triangular ruler, adds the function of drawing parallel lines, small circles and can draw angles, and is compact and easy to use.
-
Summary. A pair of triangles generally refers to an isosceles right-angled triangle with an angle of 45 degrees and a right-angled triangle with an angle of 30 degrees. So a pair of triangles has the following angles:
90 degrees, 60 degrees, 45 degrees, 30 degrees. Use a pair of triangles to draw an angle of 75 degrees, you can operate according to the following steps: first draw an edge of a 75-degree angle (draw a straight line arbitrarily), and then the hypotenuse of the isosceles right-angle triangle plate coincides with the above straight line (the hypotenuse of the triangle plate is placed on the above straight line), and then the hypotenuse of the right-angle triangle plate with a 30-degree angle angle is attached to any right-angled edge of the isosceles triangle plate (if you want the 75-degree angle to be on the left, it will be attached to the right-angled edge on the left, If you want the 75 degree angle to be on the right, then stick to the right angle) Finally, draw a straight line along the right angle of the 30 degree angle (the angle formed by this straight line and the initial straight line is 75 degrees = 45 degrees + 30 degrees) with the intersection of two straight lines as the boundary, only retain two rays in a certain direction, and the 75 degree angle is formed.
The following picture shows a diagram of a pair of triangles and drawing a 75-degree angle with a pair of triangles
How do you draw a 75° angle with a triangular ruler?
A pair of triangles generally refers to an isosceles right-angled triangle with an angle of 45 degrees and a right-angled triangle with an angle of 30 degrees. So a pair of triangles has the following angles: 90 degrees, 60 degrees, 45 degrees, 30 degrees.
Use a pair of triangles to draw an angle of 75 degrees, you can follow the following steps: first draw an edge of the 75 degree angle (draw a straight line arbitrarily), and then the hypotenuse of the isosceles right-angle triangle coincides with the above straight line (the hypotenuse of the triangle plate is placed on the above straight line), and then the hypotenuse of the right-angle triangle with an angle of 30 degrees is close to the arbitrary right-angled edge of the isosceles triangle (if you want the 75-degree angle to be on the left, it will be attached to the right-angled edge on the left, If you want the 75 degree angle to be on the right, then stick to the right angle) Finally, draw a straight line along the right angle of the 30 degree angle (the angle formed by this straight line and the initial straight line is 75 degrees = 45 degrees + 30 degrees) with the intersection of two straight lines as the boundary, only retain two rays in a certain direction, and the 75 degree angle is formed. The following picture shows a diagram of a pair of triangles and drawing a 75-degree angle with a pair of triangles
-
1. First of all, a ° is drawn from an angle.
2. The second is the ° of the combination of the two angles (15=45-30, 75=45+30, 105=45+60, 120=60+60, 135=45+90, 150=60+90).
3. Again, it is a combination of three angles: 165° (165 = 30 + 45 + 90).
4. Don't use the last corner, draw a straight line, that is, a flat angle: 180°.
Triangular ruler features.
A triangular ruler has 1 right angle and 2 acute angles.
Both acute angles of the isosceles right-angle triangular ruler are 45°. Two identical isosceles right triangles can be put together into a square, or they can be put together into a larger isosceles right triangle. The two right-angled sides of an isosceles right-angled triangular ruler are equal in length.
The acute angles of the slender triangular rulers are 30° and 60°, respectively. Two identical slender triangular rulers can be put together to form a regular triangle. The length of the hypotenuse of a slender triangle is twice the length of the short right-angled edge.
-
1. First of all, a ° is drawn from an angle.
2. The second is the ° of the combination of the two angles (15=45-30, 75=45+30, 105=45+60, 120=60+60, 135=45+90, 150=60+90).
3. Again, it is a combination of three angles: 165° (165 = 30 + 45 + 90).
4. The last corner.
No, draw a straight line, which is a flat angle: 180°.
-
In a pair of triangular rulers, in addition to two right angles, the other four acute angles are °, and the two angles on the same three-way ruler can be spelled out at right angles, and the acute angles on different triangular rulers cannot be spelled with right angles.
One: You can draw it directly:
Two: A total of 11 are drawn through the sum or difference:
-
A triangular ruler has four angles.
i.e. 30 degrees, 45 degrees, 60 degrees and 90 degrees.
Their greatest common factor is 15 degrees.
So you can draw multiples of 15 degrees.
i.e. 15 degrees, 30 degrees, 45 degrees, 60 degrees, 75 degrees, 90 degrees, 105 degrees, 120 degrees, 135 degrees, 150 degrees, 165 degrees, 180 degrees.
-
Since the degrees of each angle in a pair of triangles are °, the angles that can be obtained by combining them are: 60°-45°=15°, 60°+45°=105°, 60°+90°=150°, 90°+45°=135°, 90°+30°=120°, 30°+45°=75°.
-
The first is the ° drawn by one angle, and the second is the ° of the combination of two angles
Again, it is a combination of three angles: 165° (165 = 30 + 45 + 90) the last angle is not used, and a straight line is drawn, that is, a flat angle: 180°.
-
A triangular ruler has four angles.
i.e. 30°, 45°, 60° and 90°
Their greatest common factor is 15°
So multiples of 15° can be drawn.
i.e. 15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, 150°, 165°, 180°
-
Answer, a triangle has angles of 90 degrees, 60 degrees, 30 degrees, 45 degrees, in addition, you can also draw angles of 15 degrees, 75 degrees, 105 degrees, 120 degrees, 135 degrees, 150 degrees, 165 degrees, and 180 degrees.
Ask how to draw.
How to draw with a triangular ruler, four base angles and six combination angles.
-
° can be drawn directly;
Combinations can be drawn with ° and so on.
The slender triangle ruler is 60° in addition to the right angle of 90° and the smallest acute angle of 30°, as shown in this picture. >>>More
In modern urban residential design, foyers are often set at entrances and exits. Decorative painting is a very important thing to decorate the entrance, how to choose the size of the entrance decorative painting? The size of the foyer is mostly 136 centimeters long and 69 centimeters wide. >>>More
Composer: Lei Songde.
Lyrics: Lin Xi. >>>More