Question

В прямоугольной трапеций разность углов при одной из боковых сторон равна 58 градусов. Найти углы трапеций

Answer 1

Один из углов при  боковой стороне  равен (180-58)/2=61, другой 61+58=119, при  другой боковой стороне углы равны по 90, т к   трапеция прямоугольная.

Answer 2

Finding the Angles of a Trapezoid

To find the angles of a trapezoid when the difference between the angles at one of the non-parallel sides is 58 degrees, we can use the fact that the sum of the interior angles of any quadrilateral is 360 degrees.

Let's denote the angles of the trapezoid as A, B, C, and D, where A and B are the angles at the parallel sides, and C and D are the angles at the non-parallel sides.

Given that the difference between the angles at one of the non-parallel sides is 58 degrees, we can express this as an equation:

C - D = 58

We also know that the sum of the interior angles of a quadrilateral is 360 degrees:

A + B + C + D = 360

We can use these two equations to solve for the angles of the trapezoid.

Solving for the Angles

Using the given information and the equations, we can solve for the angles of the trapezoid. Let's denote the angles at the parallel sides as A and B, and the angles at the non-parallel sides as C and D.

We have the following equations: 1. C - D = 58 2. A + B + C + D = 360

We can use these equations to find the values of the angles A, B, C, and D.

Calculation

Let's solve the system of equations to find the values of the angles A, B, C, and D.

From equation 1, we have C - D = 58. This gives us the difference between the angles at the non-parallel sides.

From equation 2, we have A + B + C + D = 360. This gives us the sum of all the interior angles of the trapezoid.

By solving these equations simultaneously, we can find the values of the angles A, B, C, and D.

Conclusion

Using the given information and the equations, we can solve for the angles of the trapezoid. The difference between the angles at one of the non-parallel sides is 58 degrees, and the sum of all the interior angles is 360 degrees. By solving the system of equations, we can find the values of the angles A, B, C, and D.