Question

прямой угол разделили лучами исходящими из вершины на три неравных угла какие углы получились если известно что угол 1 на 24 градуса больше суммы угла 2 и угла 3 а сумма 3 и 1 угла равна 70 градусов

Answer 1

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Answer 2

Problem Analysis

We are given that a right angle is divided by rays emanating from the vertex into three unequal angles. We need to determine the measures of these angles given that angle 1 is 24 degrees larger than the sum of angles 2 and 3, and the sum of angles 3 and 1 is 70 degrees.

Solution

Let's denote the three angles as angle 1, angle 2, and angle 3. We can set up the following equations based on the given information:

1. Angle 1 is 24 degrees larger than the sum of angles 2 and 3: angle 1 = angle 2 + angle 3 + 24. 2. The sum of angles 3 and 1 is 70 degrees: angle 3 + angle 1 = 70.

To solve these equations, we can substitute the value of angle 1 from equation 1 into equation 2:

(angle 2 + angle 3 + 24) + angle 3 = 70.

Simplifying the equation, we get:

angle 2 + 2 * angle 3 = 46.

Now, we have two equations with two unknowns. We can solve this system of equations to find the values of angle 2 and angle 3.

Let's solve the system of equations:

1. From equation 1, we have: angle 1 = angle 2 + angle 3 + 24. 2. From equation 2, we have: angle 3 + angle 1 = 70.

Substituting the value of angle 1 from equation 1 into equation 2, we get:

angle 3 + (angle 2 + angle 3 + 24) = 70.

Simplifying the equation, we get:

2 * angle 3 + angle 2 = 46.

Now, we can solve this system of equations to find the values of angle 2 and angle 3.

Let's solve the system of equations:

1. From equation 1, we have: angle 1 = angle 2 + angle 3 + 24. 2. From equation 2, we have: 2 * angle 3 + angle 2 = 46.

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method:

Multiply equation 1 by 2:

2 * angle 1 = 2 * (angle 2 + angle 3 + 24).

Simplifying the equation, we get:

2 * angle 1 = 2 * angle 2 + 2 * angle 3 + 48.

Now, subtract equation 2 from the above equation:

(2 * angle 1) - (2 * angle 3 + angle 2) = (2 * angle 2 + 2 * angle 3 + 48) - (2 * angle 3 + angle 2).

Simplifying the equation, we get:

2 * angle 1 - angle 2 = angle 2 + 48.

Rearranging the equation, we get:

3 * angle 2 = 2 * angle 1 - 48.

Now, we can substitute the value of angle 2 from the above equation into equation 1 to find the value of angle 3.

Substituting the value of angle 2, we get:

angle 1 = (2 * angle 1 - 48) + angle 3 + 24.

Simplifying the equation, we get:

angle 1 = 2 * angle 1 - 24 + angle 3 + 24.

Simplifying further, we get:

angle 1 = angle 1 + angle 3.

This equation tells us that angle 1 is equal to angle 1 + angle 3, which means angle 3 is 0 degrees. However, this contradicts the given information that the three angles are unequal. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to the problem. The angles cannot be determined as the equations lead to a contradiction.