Question

Один из углов которые получаются при пересечении двух параллельных прямых секущей равен 72 градуса Найдите остальные семь углов

Answer 1

Пусть ∠1 = 72°.

При пересечении параллельных прямых секущей образуется 8 углов двух величин:

соответственные углы

∠1 = ∠5

∠3 = ∠7,

а так как ∠1 = ∠3 как вертикальные, то

∠1 = ∠5 = ∠3 = ∠7 = 72°

и соответственные углы

∠2 = ∠6

∠4 = ∠8,

а так как ∠2 = ∠4, как вертикальные, то

∠2 = ∠6 = ∠4 = ∠8

Сумма односторонних углов равна 180°, например

∠3 + ∠6 = 180°

Значит ∠6 = 180° - ∠3 = 180° - 72° = 108°.

∠1 = ∠5 = ∠3 = ∠7 = 72°

∠2 = ∠6 = ∠4 = ∠8 = 108°

Answer 2

Finding the Remaining Angles

To find the remaining seven angles formed by the intersection of two parallel lines and a transversal, we can use the fact that corresponding angles are congruent, alternate interior angles are congruent, and consecutive interior angles are supplementary.

Let's denote the given angle as angle A, which measures 72 degrees. We can use this information to find the other angles.

1. Angle A: Given as 72 degrees.

2. Corresponding Angle B: Corresponding angles are congruent, so angle B is also 72 degrees.

3. Alternate Interior Angle C: Alternate interior angles are congruent, so angle C is also 72 degrees.

4. Alternate Interior Angle D: Alternate interior angles are congruent, so angle D is also 72 degrees.

5. Consecutive Interior Angle E: Consecutive interior angles are supplementary, so angle E is 180 - 72 = 108 degrees.

6. Consecutive Interior Angle F: Consecutive interior angles are supplementary, so angle F is also 108 degrees.

7. Consecutive Interior Angle G: Consecutive interior angles are supplementary, so angle G is also 108 degrees.

8. Consecutive Interior Angle H: Consecutive interior angles are supplementary, so angle H is also 108 degrees.

Therefore, the remaining seven angles are as follows: - Angle A: 72 degrees - Angle B: 72 degrees - Angle C: 72 degrees - Angle D: 72 degrees - Angle E: 108 degrees - Angle F: 108 degrees - Angle G: 108 degrees - Angle H: 108 degrees

Please note that the angles mentioned above are based on the given information and the properties of parallel lines and transversals.