Question

Помогите!!!!! Пожалуйста!!!!!Около трапеции, один из углов которой равен 49 градусов, описана окружность. Найдите остальные углы трапеции. Если можно то с рисунком.

Answer 1

Если сумма противоположных углов четырёхугольника (трапеция-это четырёхугольник) равна 180', то около него можно описать окружность.
Тогда т.к. угол ВАD=49', то угол ВСD = 180'-49'=131'. 
Угол АВС=180'-49'=131' (т.к угол АВС и угол ВАD - односторонние). 
Угол АDC=180'-131'=49'. 

Ответ: угол А = углу D=49',  угол В = углу С = 131'. 

Answer 2

Finding the Missing Angles of a Trapezoid

To find the missing angles of a trapezoid, we need to use the properties of the trapezoid and the fact that it is circumscribed by a circle.

Let's denote the angles of the trapezoid as follows: - Angle A: the angle opposite to the longer base of the trapezoid. - Angle B: the angle opposite to the shorter base of the trapezoid. - Angle C: one of the non-parallel angles of the trapezoid. - Angle D: the other non-parallel angle of the trapezoid.

Given that one of the angles of the trapezoid is 49 degrees, we can use the following properties to find the other angles:

1. The sum of the interior angles of a trapezoid is equal to 360 degrees. 2. The opposite angles of a cyclic quadrilateral (a quadrilateral inscribed in a circle) are supplementary.

Using these properties, we can find the missing angles as follows:

1. Angle A: Since the trapezoid is circumscribed by a circle, angle A is supplementary to angle C. Therefore, angle A = 180 degrees - angle C.

2. Angle B: Angle B is supplementary to angle D. Therefore, angle B = 180 degrees - angle D.

3. Angle C: We are given that angle C is 49 degrees.

4. Angle D: Angle D is supplementary to angle B. Therefore, angle D = 180 degrees - angle B.

Now, let's calculate the values of the missing angles:

- Angle A = 180 degrees - angle C = 180 degrees - 49 degrees = 131 degrees. - Angle B = 180 degrees - angle D = 180 degrees - (180 degrees - angle B) = angle B. - Angle C = 49 degrees (given). - Angle D = 180 degrees - angle B = 180 degrees - (180 degrees - angle D) = angle D.

Therefore, the missing angles of the trapezoid are: - Angle A = 131 degrees. - Angle B = angle B. - Angle C = 49 degrees. - Angle D = angle D.

Unfortunately, I am unable to provide a diagram at the moment. However, I hope the explanation above helps you understand how to find the missing angles of a trapezoid.