Question

Сумма противолежащих углов равна 146 градусов . Найдите углы ромба .

Answer 1

Противолежащие углы ромба равны между собой
146°:2=73° - острый угол ромба
180°-73°=107° - тупой угол ромба

Answer 2

Finding the Angles of a Rhombus

To find the angles of a rhombus when the sum of opposite angles is given, we can use the fact that the sum of all angles in any quadrilateral is 360 degrees.

Let's denote the angles of the rhombus as A, B, C, and D. Given that the sum of opposite angles is 146 degrees, we can set up the following equation:

A + C = 146 (opposite angles)

Since a rhombus has four equal sides, it also has four equal angles. Therefore, we can express the other two angles in terms of A and C:

B = A (opposite angles are equal) D = C (opposite angles are equal)

Now, we can use the fact that the sum of all angles in a quadrilateral is 360 degrees to find the values of A, B, C, and D.

Calculating the Angles

Using the information above, we can calculate the angles of the rhombus:

1. From the equation A + C = 146, we can express C in terms of A: C = 146 - A.

2. Since B = A and D = C, we can express B and D in terms of A: B = A and D = 146 - A.

3. Now, we can use the fact that the sum of all angles in a quadrilateral is 360 degrees to find the value of A: A + B + C + D = 360 Substituting the expressions for B and D: A + A + (146 - A) + (146 - A) = 360 Simplifying: 4A + 292 = 360 4A = 68 A = 17

Results

So, the angles of the rhombus are: - A = 17 degrees - B = 17 degrees - C = 146 - A = 146 - 17 = 129 degrees - D = 146 - A = 146 - 17 = 129 degrees

Therefore, the angles of the rhombus are: A = 17°, B = 17°, C = 129°, and D = 129°.