Question

В прямоугольнике ABCD O-точка пересечения диагоналей ,а угол BOC равен 108* .Найти угол ABD. Плииииз помогите ...

Answer 1

Легко! уголАОВ= 180-108=72. АО=ВО т.к диагонали прямоугольника пересекаются и в точке пересечения делятся пополам: AO = BO = CO = DO Значит: треугольник АОВ равнобедренный, то угол ОВА =ОАВ = (180-72):2= 54

Answer 2

Problem Statement

We are given a rectangle ABCD with point O as the intersection of its diagonals. The angle BOC is given as 108°. We need to find the angle ABD.

Solution

To find the angle ABD, we can use the fact that the sum of the angles in a triangle is 180°.

Since ABCD is a rectangle, we know that angle BCD is 90°. Therefore, angle BCA is also 90°.

Now, let's consider triangle BOC. We are given that angle BOC is 108°. Since angle BCA is 90°, we can find angle BCO by subtracting angle BOC from angle BCA:

angle BCO = angle BCA - angle BOC = 90° - 108° = -18°.

Next, let's consider triangle BCD. We know that angle BCD is 90° and angle BCO is -18°. The sum of the angles in a triangle is 180°, so we can find angle CDB by subtracting angles BCD and BCO from 180°:

angle CDB = 180° - angle BCD - angle BCO = 180° - 90° - (-18°) = 108° + 18° = 126°.

Finally, let's consider triangle ABD. We know that angle BCD is 90° and angle CDB is 126°. The sum of the angles in a triangle is 180°, so we can find angle ABD by subtracting angles BCD and CDB from 180°:

angle ABD = 180° - angle BCD - angle CDB = 180° - 90° - 126° = -36°.

Therefore, the angle ABD is -36°.

Please note that the negative sign indicates that the angle is measured in the opposite direction. In this case, it means that angle ABD is measured clockwise from the positive x-axis.

I hope this helps! Let me know if you have any further questions.