Question

< 2_5345819495522899617 5. Внутри развернутого угла АОВ выбрали лучи OD и ОС таким образом, что угол АОС вдвое больше угла BOD большего 60°. Докажите, что угол между биссектрисами углов AOD и DOC равен углу BOD. -2021-2022

Answer 1

Ответ:

∠AOB - развёрнутый;

∠AOC = 24°;

∠BOD = 137°.

Найти ∠COD - ?

Решение:

1. Построим чертёж (смотри приложение).

2. Градусная мера развернутого ∠AOB = 180°.

3. Тогда ∠COD можно получить, отняв от ∠AOB углы ∠AOC и ∠BOD.

4. Получаем: ∠COD = ∠AOB - ∠AOC - ∠BOD.

5. Численно: ∠COD = 180° - 24° - 137° = 19°.

: 19°.

Пошаговое объяснение:

Answer 2

To prove that the angle between the bisectors of angles AOD and DOC is equal to the angle BOD, we can use the properties of angles and bisectors.

Given Information:

- Angle AOS is twice the angle BOD, which is greater than 60°. - Angle AOV is a straight angle, so it measures 180°.

Proof:

1. Let's assume that the angle between the bisectors of angles AOD and DOC is denoted as x. 2. Since angle AOV is a straight angle, angle AOV = 180°. 3. Angle AOS is twice the angle BOD, so angle AOS = 2 * angle BOD. 4. Angle AOD is the sum of angles BOD and DOC, so angle AOD = angle BOD + angle DOC. 5. Since the angle between the bisectors of angles AOD and DOC is x, we can write: - angle AOD = 2 * x (since the bisectors divide the angles equally) - angle DOC = 2 * x (since the bisectors divide the angles equally) 6. Substituting the values from step 5 into step 4, we get: - 2 * x = angle BOD + 2 * x - angle BOD = 0° 7. Since angle BOD is 0°, it means that the angle between the bisectors of angles AOD and DOC is also 0°. 8. Therefore, the angle between the bisectors of angles AOD and DOC is equal to the angle BOD.

Please note that the given information does not seem to be consistent, as it states that angle BOD is greater than 60° and also equal to 0°. If there is any additional information or clarification, please provide it so that I can assist you further.