Question

Найдите углы треугольника, если внешние углы при двух вершинах равна по 160∘. Помогите срочно даю 20 баллов​

Answer 1

Ответ:

20°, 20°, 140° - углы треугольника

Объяснение:

Пусть дан треугольник Δ АВС . По условию внешние углы при двух вершинах равны 160°. Тогда ∠ МАВ =∠ MCD =160°.

Угол, смежный с внутренним углом треугольника, называется внешним углом треугольника. Так как сумма смежных углов равна 180°, то  ∠ А=∠С =180°-160°=20°.

Сумма углов треугольника равна 180 °.

Тогда ∠В= 180°-(20°+20°)= 180°-40°=140°.

Answer 2

Ответ:

Углы треугольника АВС: ∠ВАС = 20°; ∠ВСА = 20°; ∠АВС = 140°.

Объяснение:

Требуется найти углы треугольника, если внешние углы при двух вершинах равна по 160°.

Дано: ΔАВС;

∠МАВ = ∠КСВ = 160° - внешние.

Найти: углы ΔАВС.

Решение:

• Сумма смежных углов равна 180°.

⇒ ∠ВАС = 180° - ∠МАВ = 180° - 160° = 20° (смежные);

∠ВСА = 180° - ∠КСВ = 180° - 160° = 20° (смежные).

• Сумма углов треугольника равна 180°.

∠АВС = 180° - ∠ВАС - ∠ВСА = 180° - 20° - 20° = 140°

Нашли углы треугольника АВС: ∠ВАС = 20°; ∠ВСА = 20°; ∠АВС = 140°.

Answer 3

Finding the Angles of a Triangle

To find the angles of a triangle when the external angles at two vertices are both 160 degrees, we can use the fact that the sum of the measures of the three exterior angles of any triangle is always 360 degrees.

Given that the external angles at two vertices are 160 degrees, we can calculate the internal angles of the triangle using the following steps:

1. Calculate the Third External Angle: - Since the sum of the measures of the three exterior angles of any triangle is 360 degrees, we can find the measure of the third external angle by subtracting the sum of the two given external angles from 360 degrees.

2. Use the Relationship Between External and Internal Angles: - The relationship between the external and internal angles of a triangle is that the external angle and its corresponding internal angle add up to 180 degrees.

3. Calculate the Internal Angles: - Once we have the measure of the third external angle, we can use the relationship mentioned above to find the measures of the internal angles of the triangle.

Calculation

Let's proceed with the calculations:

1. Calculate the Third External Angle: - 360° - (160° + 160°) = 40°

2. Use the Relationship Between External and Internal Angles: - Since the external angle and its corresponding internal angle add up to 180 degrees, the internal angles at the two vertices with external angles of 160 degrees are: - 180° - 160° = 20°

3. Calculate the Internal Angles: - Given that the sum of the internal angles of a triangle is always 180 degrees, we can find the third internal angle by subtracting the sum of the two known internal angles from 180 degrees: - 180° - (20° + 20°) = 140°

Conclusion

Therefore, the angles of the triangle, when the external angles at two vertices are both 160 degrees, are: - 20°, 20°, and 140°.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.