Question

Дан параллелограмм ABCD, угл A =60 градусов, сторона AB=16cм, а AD=29см. Найти периметр (ABCD) и углы параллелограмма?

Answer 1

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Answer 2

Угол А=В=60°
Угол В=D=120°
AB=CD=16cм
AD=BC=29см

Answer 3

Given Information

We are given a parallelogram ABCD with angle A measuring 60 degrees, side AB measuring 16 cm, and side AD measuring 29 cm. We need to find the perimeter of the parallelogram and the angles of the parallelogram.

Perimeter of the Parallelogram

To find the perimeter of the parallelogram, we need to add the lengths of all four sides. Since opposite sides of a parallelogram are equal in length, we can find the perimeter by multiplying the length of one side by 2 and adding it to the length of the adjacent side.

Let's denote the length of side AB as a and the length of side AD as b. The perimeter (P) of the parallelogram ABCD can be calculated using the formula: P = 2(a + b).

In this case, a = 16 cm and b = 29 cm. Substituting these values into the formula, we get:

P = 2(16 + 29) = 2(45) = 90 cm.

Therefore, the perimeter of the parallelogram ABCD is 90 cm.

Angles of the Parallelogram

In a parallelogram, opposite angles are equal. Since angle A is given as 60 degrees, we know that angle C is also 60 degrees.

To find the other two angles, we can use the fact that the sum of the interior angles of a parallelogram is always 360 degrees. Since angles A and C are both 60 degrees, the sum of angles B and D must be 360 - 60 - 60 = 240 degrees.

Therefore, angles B and D are both 240/2 = 120 degrees.

In summary, the angles of the parallelogram ABCD are as follows: - Angle A = 60 degrees - Angle B = 120 degrees - Angle C = 60 degrees - Angle D = 120 degrees.

Please let me know if there is anything else I can help you with.