Question

Найдите угол В четырех угольника АВСД вписанного в окружность если угол В=2 углу Д. Ответ дайте в градусах.

Answer 1

В+Д=180 2Д+Д=180 3Д=180 Д=180:3=60 В=2*60=120 Ответ120

Answer 2

Finding the Angle in a Inscribed Quadrilateral

To find the angle B in the inscribed quadrilateral ABCD, given that angle B is twice angle D, we can use the properties of inscribed angles in a circle.

In an inscribed quadrilateral, opposite angles are supplementary, meaning they add up to 180 degrees. Therefore, we can set up the following equation:

B + D = 180 degrees

Since we know that angle B is twice angle D, we can substitute 2D for B in the equation:

2D + D = 180 degrees

Combining like terms, we get:

3D = 180 degrees

To solve for D, we divide both sides of the equation by 3:

D = 60 degrees

Now that we have the value of D, we can substitute it back into the equation to find the value of B:

B = 2D = 2 * 60 degrees = 120 degrees

Therefore, angle B in the inscribed quadrilateral ABCD is 120 degrees.