Question

Один из углов параллелограмма в два раза меньше другого его угла. Найдите все углы параллелограмма.

Answer 1

Х - острый угол параллелограмма
2х - тупой угол параллелограмма
сумма острого и тупого углов параллелограмма равна 180°
х + 2х = 180
3х = 180
х = 60
2х = 120
Ответ: два тупых угла параллелограмма по 120° и два острых - по 60°

Answer 2

Finding the angles of a parallelogram

To find the angles of a parallelogram, we need to know that opposite angles in a parallelogram are congruent. Let's denote one of the angles as x. According to the given information, one of the angles is twice as small as the other angle. Therefore, the other angle can be represented as 2x.

Since the sum of the interior angles of any quadrilateral is 360 degrees, we can set up the following equation:

x + 2x + x + 2x = 360

Simplifying the equation, we get:

6x = 360

Dividing both sides of the equation by 6, we find:

x = 60

Now that we know the value of x, we can find the measure of the other angle:

2x = 2 * 60 = 120

Therefore, the angles of the parallelogram are:

- One angle: 60 degrees - Opposite angle: 120 degrees

Please note that the angles of a parallelogram can vary depending on the specific parallelogram in question. However, based on the given information, these are the angles that satisfy the given conditions.