Question

При перетині двох паралельних прямою утворилися 8 кутів. Різниця між двома з них 90градусів. Знайти градусну міру всіх кутів що утворилися.

Answer 1

Сначала кут 1 - кут 2 = 90 и потом рівняння :
x+x+90=180 (за суміжністю, так як не сказано що вони рівні)
решаешь его и потом ищешь другие кут за суміжністю і вертикальністю

Answer 2

Given Information:

- Two parallel lines intersect to form 8 angles. - The difference between two of these angles is 90 degrees.

Solution:

To find the degree measure of all the angles formed, we need to determine the degree measure of each individual angle.

Let's assume that the two intersecting lines are line AB and line CD. The points of intersection are point E and point F.

We can label the angles formed as follows: - Angle 1: AEF - Angle 2: BEF - Angle 3: CEF - Angle 4: DEF - Angle 5: AED - Angle 6: BEC - Angle 7: CED - Angle 8: BED

Since the two intersecting lines are parallel, we know that Angle 1 and Angle 5 are corresponding angles, and Angle 2 and Angle 6 are corresponding angles. Corresponding angles are congruent, meaning they have the same degree measure.

Given that the difference between Angle 1 and Angle 2 is 90 degrees, we can conclude that Angle 1 is 90 degrees larger than Angle 2.

Let's assume that Angle 2 has a degree measure of x degrees. Therefore, Angle 1 has a degree measure of (x + 90) degrees.

Since Angle 1 and Angle 5 are corresponding angles, they have the same degree measure. Therefore, Angle 5 also has a degree measure of (x + 90) degrees.

Similarly, Angle 2 and Angle 6 are corresponding angles, so Angle 6 has a degree measure of x degrees.

Now, we can determine the degree measure of the remaining angles.

Since the sum of the degree measures of angles around a point is 360 degrees, we can set up the following equation: (x + 90) + x + x + (x + 90) + x + x + x = 360

Simplifying the equation, we get: 6x + 270 = 360

Subtracting 270 from both sides, we have: 6x = 90

Dividing both sides by 6, we find: x = 15

Therefore, Angle 2 has a degree measure of 15 degrees, and Angle 1 has a degree measure of (15 + 90) = 105 degrees.

Using this information, we can determine the degree measure of all the angles: - Angle 1: 105 degrees - Angle 2: 15 degrees - Angle 3: 105 degrees - Angle 4: 15 degrees - Angle 5: 105 degrees - Angle 6: 15 degrees - Angle 7: 105 degrees - Angle 8: 15 degrees

So, the degree measure of all the angles that were formed is as follows: - Angle 1: 105 degrees - Angle 2: 15 degrees - Angle 3: 105 degrees - Angle 4: 15 degrees - Angle 5: 105 degrees - Angle 6: 15 degrees - Angle 7: 105 degrees - Angle 8: 15 degrees

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