Question

При пересечении двух прямых из одних из полученных углов равен 75 градусов Найдите градусные меры остальных углов Помогите пожалуйста

Answer 1

Вертикальные углы (75°) равны

Answer 2

Finding the Degree Measures of the Other Angles

To find the degree measures of the other angles when two lines intersect and one of the resulting angles is 75 degrees, we need to consider the properties of intersecting lines and angles.

When two lines intersect, they form four angles at the intersection point. These angles are known as vertical angles and are congruent, meaning they have the same measure. Additionally, the sum of the measures of adjacent angles formed by intersecting lines is always 180 degrees.

Let's label the angles formed by the intersection of the two lines as follows:

- Angle 1: The angle whose measure is given as 75 degrees. - Angle 2: The angle adjacent to Angle 1. - Angle 3: The angle opposite to Angle 1. - Angle 4: The angle adjacent to Angle 3.

Since Angle 1 and Angle 3 are vertical angles, they have the same measure. Therefore, Angle 3 is also 75 degrees.

To find the measure of Angle 2, we can subtract the sum of Angle 1 and Angle 3 from 180 degrees:

Angle 2 = 180 degrees - (Angle 1 + Angle 3) Angle 2 = 180 degrees - (75 degrees + 75 degrees) Angle 2 = 180 degrees - 150 degrees Angle 2 = 30 degrees

Similarly, Angle 4 is also 30 degrees because it is adjacent to Angle 3.

Therefore, the degree measures of the other angles are as follows:

- Angle 1: 75 degrees - Angle 2: 30 degrees - Angle 3: 75 degrees - Angle 4: 30 degrees

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