Question

Углы АОВ и ВОС смежные, луч ОD биссектриса угла АОВ, угол BOD на 18 градусов меньше угла ВОС. Найдите углы АОВ и ВОС.

Answer 1

Обозначим угол AOB за 2x. Тогда каждый из углов AOD и BOD равен x, а BOC по условию равен x+18. Так как сумма смежных углов равна 180 градусам, угол BOC также равен 180-2x. Решая уравнение x+18=180-2x, получаем x=54. Значит, угол AOB равен 108 градусам, а угол BOС равен 180-108=72 градусам.

Answer 2

Given Information

The angles AOB and BOC are adjacent, the ray OD is the bisector of angle AOB, and the angle BOD is 18 degrees less than the angle BOC.

Solution

To find the angles AOB and BOC, we can use the information provided.

First, let's denote: - Angle AOB as x - Angle BOC as y

We know that the angle BOD is 18 degrees less than the angle BOC, so we can express it as: - Angle BOD = y - 18

Since the ray OD is the bisector of angle AOB, we can use the property that the bisector divides the angle into two equal angles. Therefore: - Angle AOD = Angle BOD

Now, we can use the fact that the sum of angles in a straight line is 180 degrees to find the values of x and y.

Calculation

Using the given information and the properties of angles, we can set up the following equations: 1. x + y = 180 (angles AOB and BOC form a straight line) 2. y - 18 = y - x (angle BOD is 18 degrees less than angle BOC, and the ray OD bisects angle AOB)

Solving these equations will give us the values of x and y, which represent the angles AOB and BOC, respectively.

Let's proceed with the calculations.