Question

Есть большой угол 100 градусов, у него внутри расположены 2 луча, которые делят его в отношении 1:2:7. Нарисуй рисунок и вычисли градусы неизвестных углов. Срочно, (контрольная) ​

Answer 1

1) 1 + 2 + 7 = 10 частей всего в разделении угла 100°.
2) 100 : 10 = 10° - соответствуют одной части и, таким образом, одному из искомых углов, который в отношении обозначен числом 1.
3) 10 • 2 = 20° - второй из искомых углов.
3) 10 • 7 = 70° - третий из искомых углов.

Ответ: 10°, 20°; 70°.

Answer 2

Problem Analysis

We have a large angle measuring 100 degrees, and it is divided by two rays in a ratio of 1:2:7. We need to draw a diagram and calculate the measures of the unknown angles.

Solution

To solve this problem, let's start by drawing a diagram:

          A
         / \
        /   \
       /     \
      /       \
     /         \
    /           \
   /_____________\
  B       C       D

In the diagram above, we have angle A, which measures 100 degrees. This angle is divided by two rays into three parts in the ratio of 1:2:7. Let's label the angles as follows:

- Angle B: The angle formed by the first ray. - Angle C: The angle formed by the second ray. - Angle D: The angle formed by the third ray.

Now, let's calculate the measures of the unknown angles.

Calculation

Since the ratio of the angles is 1:2:7, we can set up the following equation:

1x + 2x + 7x = 100

Simplifying the equation, we get:

10x = 100

Dividing both sides of the equation by 10, we find:

x = 10

Now, we can substitute the value of x back into the equation to find the measures of the angles:

- Angle B: 1x = 1 * 10 = 10 degrees. - Angle C: 2x = 2 * 10 = 20 degrees. - Angle D: 7x = 7 * 10 = 70 degrees.

Therefore, the measures of the unknown angles are:

- Angle B: 10 degrees. - Angle C: 20 degrees. - Angle D: 70 degrees.

Conclusion

In summary, the measures of the unknown angles in the given diagram are as follows:

- Angle B: 10 degrees. - Angle C: 20 degrees. - Angle D: 70 degrees.

Please note that this solution is based on the given information and the assumption that the angles are adjacent and form a straight line.