Question

Сумма двух углов 160°. Докажите,  что эти углы не могут быть смежными.​

Answer 1

Сумма смежных углов всегда равна 180°, исходя из определения:

Смежные углы — это два угла, у которых одна сторона общая, а две другие дополняют друг друга до прямой. Таким образом, вместе смежные углы составляют развёрнутый угол, и сумма их угловых величин всегда равна 180°.

Answer 2

Sum of Two Angles is 160°

To prove that two angles cannot be adjacent, we need to understand the concept of adjacent angles and how their sum relates to 180°.

Adjacent angles are two angles that share a common vertex and a common side but do not overlap. When two adjacent angles are added together, their sum is always equal to 180°.

Let's assume that the sum of two angles is 160°. To prove that these angles cannot be adjacent, we will show that their sum is not equal to 180°.

Proof:

Let's assume the two angles are angle A and angle B.

Step 1: Assume angle A is x°.

Step 2: Since the sum of the two angles is 160°, we can express angle B in terms of angle A: angle B = 160° - x°.

Step 3: Now, let's consider the sum of angle A and angle B: angle A + angle B = x° + (160° - x°) = 160°.

Step 4: Since the sum of angle A and angle B is 160°, which is not equal to 180°, we can conclude that these angles cannot be adjacent.

Therefore, we have proved that if the sum of two angles is 160°, they cannot be adjacent angles.

Please note that this proof assumes that the angles are measured in degrees and follows the conventional understanding of adjacent angles.