Question

Помогите пожалуйста решить задачу. Задача: Угол обзора между ромба высотах, которые взяты из одной вершины, 84°. Вычисли углы ромба!

Answer 1

Ответ:

2 угла 84, 2 угла 96

Пошаговое объяснение:

1. 1 угол ромба 84

Т.к. углы в ромбе попарно равны, то 2 угол тоже 84

2. 84+84= 168

3. 360-168= 192

4.192:2= 96

Answer 2

Problem Analysis

We are given that the angle between the heights of a rhombus, taken from one vertex, is 84°. We need to find the angles of the rhombus.

Solution

To solve this problem, we can use the properties of a rhombus. In a rhombus, opposite angles are equal, and the sum of all angles is 360°.

Let's assume that the angles of the rhombus are A, B, C, and D. Since opposite angles are equal, we have A = C and B = D.

We know that the angle between the heights of the rhombus, taken from one vertex, is 84°. This angle is formed by two adjacent angles of the rhombus. Let's call these angles X and Y.

From the given information, we can deduce that X + Y = 84°.

Since the sum of all angles in a rhombus is 360°, we have A + B + C + D = 360°.

Substituting A = C and B = D, we get A + B + A + B = 360°.

Simplifying the equation, we have 2A + 2B = 360°.

Dividing both sides of the equation by 2, we get A + B = 180°.

We can rewrite this equation as A = 180° - B.

Substituting this value of A in the equation X + Y = 84°, we get (180° - B) + (180° - B) = 84°.

Simplifying the equation, we have 360° - 2B = 84°.

Subtracting 360° from both sides of the equation, we get -2B = -276°.

Dividing both sides of the equation by -2, we get B = 138°.

Substituting this value of B in the equation A = 180° - B, we get A = 180° - 138° = 42°.

Since A = C and B = D, the angles of the rhombus are 42°, 138°, 42°, and 138°.

Therefore, the angles of the rhombus are 42°, 138°, 42°, and 138°.

Answer

The angles of the rhombus are 42°, 138°, 42°, and 138°.