Question

Помогите ,срочно!!!! Четырехугольник АВСD вписан в окружность. Угол АВС равен 54 градусов, угол САD равен 41 градус. Найдите угол АВД. Ответ дайте в градусах.

Answer 1

Дуга АС проходящая через Д равна 54*2=108 (угол равен половине диагонали)
дуга СД=82
дуга АС=АД+ДС
дуга АД=108-82=26
угол АВД опирается на дугу АД и равен ее половине 26/2=13 градусов

Answer 2

Problem Analysis

We are given a quadrilateral ABCD inscribed in a circle. We know that angle ABC is 54 degrees and angle CAD is 41 degrees. We need to find angle ABD.

Solution

To find angle ABD, we can use the property that the opposite angles in an inscribed quadrilateral are supplementary. This means that the sum of angle ABC and angle ABD is equal to 180 degrees.

Let's denote angle ABD as x. Then we have the equation:

x + 54 = 180

Solving for x, we subtract 54 from both sides:

x = 180 - 54

Calculating the value of x:

x = 126 degrees

Therefore, angle ABD is 126 degrees.

Conclusion

The angle ABD in the quadrilateral ABCD, which is inscribed in a circle, is 126 degrees.