Question

Знайдіть кути, які утворюються в результаті перетину двох прямих, якщо сума трьох з них 270°​

Answer 1

Ответ:

∠1 = 90°; ∠2 = 90°;  ∠3 = 90°;  ∠4 = 90°;

Пошаговое объяснение:

Сумма всех углов равна 360°

По условию, ∠1 + ∠2 + ∠3 = 270° - сумма трёх углов

Найти: ∠1; ∠2; ∠3; ∠4.

∠1 + ∠2 + ∠3 + ∠4 = 360°

(∠1 + ∠2 + ∠3) + ∠4 = 360°

270° + ∠4 = 360°

∠4 = 360° − 270°

∠4 = 90°

∠2 = ∠4 = 90° - вертикальные углы

∠4 и ∠3 − смежные, значит: ∠4 + ∠3 = 180°

90° + ∠3 = 180°

∠3 = 180° - 90°;  ∠3 = 90°; ∠1 = ∠3 = 90° − углы вертикальные

Answer 2

Finding the angles formed by the intersection of two lines

To find the angles formed by the intersection of two lines, we need to consider the properties of intersecting lines and the relationships between the angles they form.

Let's assume we have two lines, Line 1 and Line 2, that intersect at a point O. The angles formed by the intersection of these lines can be classified into four types:

1. Vertical angles: Vertical angles are formed by two intersecting lines and are opposite each other. They have equal measures. In other words, if angle A is formed by Line 1 and Line 2, and angle B is formed by Line 1 and Line 3 (a line parallel to Line 2), then angle A is congruent to angle B.

2. Adjacent angles: Adjacent angles are formed by two intersecting lines and share a common side. The sum of adjacent angles formed by two intersecting lines is always 180 degrees. In other words, if angle A and angle B are adjacent angles formed by Line 1 and Line 2, then the measure of angle A + the measure of angle B = 180 degrees.

3. Supplementary angles: Supplementary angles are formed by two intersecting lines and are adjacent to each other. The sum of supplementary angles formed by two intersecting lines is always 180 degrees. In other words, if angle A and angle B are supplementary angles formed by Line 1 and Line 2, then the measure of angle A + the measure of angle B = 180 degrees.

4. Complementary angles: Complementary angles are formed by two intersecting lines and are adjacent to each other. The sum of complementary angles formed by two intersecting lines is always 90 degrees. In other words, if angle A and angle B are complementary angles formed by Line 1 and Line 2, then the measure of angle A + the measure of angle B = 90 degrees.

Now, let's consider the given information that the sum of three angles formed by the intersection of two lines is 270 degrees. Based on this information, we can make the following observations:

- If the three angles are adjacent angles, their sum would be 180 degrees, not 270 degrees. - If the three angles are supplementary angles, their sum would be 180 degrees, not 270 degrees. - If the three angles are complementary angles, their sum would be 90 degrees, not 270 degrees.

Therefore, it seems that the given information contradicts the properties of intersecting lines and the relationships between the angles they form. It is not possible for the sum of three angles formed by the intersection of two lines to be 270 degrees.

Please let me know if there is anything else I can help you with!