Question

Углы АОБ и БОС- смежные. Найдите угол АОБ, если угол БОС в 1,5 раза меньше угла АОБ.​

Answer 1

Ответ:

составим уравнение:

x - часть угла

x+1.5x=180

2.5x=180

x= 180/2.5

x= 72

ответ: первый угол 72., второй 108 (АОБ)

Объяснение:

Answer 2

Finding the Angle AOB

To find the angle AOB, we need to use the information given: the angle BOS is 1.5 times smaller than the angle AOB.

Let's assume that the angle AOB is x degrees. According to the given information, the angle BOS is 1.5 times smaller, so the angle BOS is (1/1.5) * x = (2/3) * x degrees.

Since the angles AOB and BOS are adjacent angles, their sum should be equal to 180 degrees. Therefore, we can write the equation:

x + (2/3) * x = 180

To solve this equation, we can combine like terms:

(5/3) * x = 180

Now, we can isolate x by multiplying both sides of the equation by (3/5):

x = (180 * 3) / 5

Simplifying the expression:

x = 108 degrees

Therefore, the angle AOB is 108 degrees.

Conclusion

The angle AOB is 108 degrees, given that the angle BOS is 1.5 times smaller than the angle AOB.