Question

Найдите углы равнобедренной трапеции, если один из ее углов в 2 раза больше другого

Answer 1

Один угол х. Другой в два раза больше - 2х. Трапеция равнобедренная. Третий угол равен первому х. Четвертый равен второму 2х. Сумма углов 360.
Решаешь уравнение х + х + 2х + 2х = 360
6х = 360
х = 360 : 60
х = 60 

хначит 2х = 2 х 60 = 120

Ответ: 60, 60, 120, 120

Answer 2

Finding the Angles of an Isosceles Trapezoid

To find the angles of an isosceles trapezoid when one angle is twice the other, we can use the properties of trapezoids and the relationship between the angles.

Step 1: Identify the Relationship Between the Angles Let's denote the smaller angle as x and the larger angle as 2x. According to the given information, one angle is twice the other.

Step 2: Use the Property of Isosceles Trapezoid In an isosceles trapezoid, the base angles (the angles formed by one of the non-parallel sides and a parallel side) are congruent.

Step 3: Set Up the Equation We can use the fact that the sum of the interior angles of a trapezoid is 360 degrees to set up an equation.

Step 4: Solve for the Angles By solving the equation, we can find the values of the angles.

Calculation

Let's solve for the angles using the given information and the steps outlined above.

We have: - One angle = x - Another angle = 2x

Using the fact that the sum of the interior angles of a trapezoid is 360 degrees, we can set up the equation: x + x + 2x + 2x = 360

Solving for x: 6x = 360 x = 60

So, the smaller angle (x) is 60 degrees, and the larger angle (2x) is 120 degrees.

Therefore, the angles of the isosceles trapezoid are 60 degrees and 120 degrees.

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