Question

Визначити кути рівнобічної трапеції, якщовідомо, що різниця протилежних кутів дорівнює 40гр.

Answer 1

Х+х+40=180
2х=180-40
2х=140
х=140/2
х=70 град при одной основе
180-70=40 град при другой

Answer 2

Finding the Angles of an Isosceles Trapezoid

To find the angles of an isosceles trapezoid when the difference between opposite angles is known, we can use the fact that the sum of the interior angles of any quadrilateral is 360 degrees.

Let's denote the two equal angles of the trapezoid as x and the other two angles as y. Given that the difference between opposite angles is 40 degrees, we can set up the following equation:

x - y = 40

Since the trapezoid is isosceles, the two equal angles can be denoted as x. Therefore, the sum of the interior angles can be expressed as:

x + x + y + y = 360

Solving these two equations simultaneously will allow us to find the values of x and y.

Solving for the Angles

Let's solve the system of equations to find the values of x and y.

From the equation x - y = 40, we can express y in terms of x as y = x - 40.

Substituting this expression for y into the equation x + x + y + y = 360, we get:

2x + 2(x - 40) = 360

Solving for x:

2x + 2x - 80 = 360

4x - 80 = 360

4x = 440

x = 110

Now that we have found the value of x, we can find the value of y using the equation y = x - 40:

y = 110 - 40

y = 70

Conclusion

Therefore, the angles of the isosceles trapezoid are: - x = 110 degrees - y = 70 degrees