Question

Знайди кути чотирикутника, якщо один з них менший від другого, третього і четвертого відповідно на 10 градусів, 20 і 30 градусів

Answer 1

пусть х*-1 кут

тогда (х+10)*- 2 ут

(х+20)*-3 кут

(х+30)*-4 кут

за теоремою про суми кутів чотирикутника(=180*) маємо

х+х+10+х+20+х+30=360

4х+60=360

х=75* 1 ут

х+10=85* 2 кут

х+20=95*  кут

х+30=105* 4 кут 

Answer 2

Пусть наименьший угол равен х, тогда три остальные равны соответственно (х+10), (х+20), (х+30).

Сумма внутренних углов 4-хугольника равна 180*(4-2)=180*2=360 градусов, значит

х+х+10+х+20+х+30=360;   4х+60=360;   4х=300;   х=300/4=75 градусов.

Второй угол равен 75+10=85, третий 75+20=95, четвертый 75+30=105 градусов.

ОТВЕТ: 75, 85, 95, 105 градусов.

Answer 3

Finding the angles of a quadrilateral

To find the angles of a quadrilateral when one angle is smaller than the others by 10 degrees, the second angle is smaller than the third angle by 20 degrees, and the fourth angle is smaller than the third angle by 30 degrees, we can use the following steps:

1. Let's assume the angles of the quadrilateral are A, B, C, and D, in clockwise order. 2. According to the given conditions, we have the following equations: - A = B + 10 - B = C + 20 - D = C + 30 3. We can substitute the values of B and D in terms of C into the equation for A to get a single equation in terms of C. 4. Solving the equation will give us the value of C. 5. Once we have the value of C, we can substitute it back into the equations for B and D to find their values. 6. Finally, we can calculate the value of A by substituting the value of B into the equation for A.

Let's solve the equations step by step:

1. Let A, B, C, and D be the angles of the quadrilateral. 2. According to the given conditions, we have: - A = B + 10 - B = C + 20 - D = C + 30 Substituting the values of B and D into the equation for A, we get:

A = (C + 20) + 10 A = C + 30

Now we have a single equation in terms of C. Solving this equation will give us the value of C.

Let's solve the equation:

C + 30 = C + 30

The equation is true for any value of C. This means that the value of C can be any real number.

Once we have the value of C, we can substitute it back into the equations for B and D to find their values.

B = C + 20 D = C + 30

Finally, we can calculate the value of A by substituting the value of B into the equation for A:

A = B + 10

Since B = C + 20, we have:

A = (C + 20) + 10 A = C + 30

Therefore, the angles of the quadrilateral are as follows:

A = C + 30 B = C + 20 C can be any real number D = C + 30

Please note that the value of C can be any real number, which means there are infinitely many possible quadrilaterals that satisfy the given conditions.

I hope this helps! Let me know if you have any further questions.