Question

Разность углов, при­ле­жа­щих к одной сто­ро­не параллелограмма, равна 30 Най­ди­те мень­ший угол параллелограмма. Ответ дайте в градусах. ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Ответ:      75° .

Объяснение:

ABCD  - паралелограм ; ∠В - ∠А = 30° .Як відомо у паралелограмі

                                          ∠В + ∠А = 180°; додаємо рівняння системи :

    2∠В = 210° ;       ∠В = 210° : 2 = 105° ;  ∠А = 180° - ∠В = 180°- 105° = 75° .

Answer 2

Finding the Smallest Angle of a Parallelogram

To find the smallest angle of a parallelogram, we need to understand the properties of parallelograms and how angles are related within them.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal. In other words, if we label the angles of a parallelogram as A, B, C, and D, then angle A is equal to angle C, and angle B is equal to angle D.

In this case, we are given that the difference between the angles adjacent to one side of the parallelogram is 30 degrees. Let's assume that the angles adjacent to this side are A and B, with A being the larger angle. Therefore, the difference between A and B is 30 degrees.

Since opposite angles in a parallelogram are equal, we can conclude that angle C is also equal to angle A, and angle D is equal to angle B.

To find the smallest angle of the parallelogram, we need to determine the value of angle B. Since the difference between A and B is 30 degrees, we can express angle A in terms of angle B as follows:

A = B + 30

Since the sum of the angles in a parallelogram is 360 degrees, we can write the equation:

A + B + C + D = 360

Substituting the values of A and B, we get:

(B + 30) + B + (B + 30) + B = 360

Simplifying the equation, we have:

4B + 90 = 360

Subtracting 90 from both sides, we get:

4B = 270

Dividing both sides by 4, we find:

B = 67.5

Therefore, the smallest angle of the parallelogram is 67.5 degrees.

Please let me know if you have any further questions!