Question

Докажите что если А и Б- смежные , то 2|A-90°|=|a-b|​

Answer 1

Ответ:

Объяснение:

180-90=90

Answer 2

Proof that if A and B are adjacent, then 2|A-90°|=|a-b|

To prove the given statement, let's consider two adjacent angles A and B.

By definition, adjacent angles are two angles that share a common vertex and a common side but do not overlap. In this case, A and B are adjacent angles.

Let's assume that A is the larger angle and B is the smaller angle.

We know that the sum of adjacent angles is equal to 180 degrees. Therefore, we can write the equation:

A + B = 180°

Now, let's rearrange the equation to isolate A:

A = 180° - B

Next, let's substitute A in the equation 2|A-90°|=|a-b|:

2|(180° - B) - 90°| = |A - B|

Simplifying further:

2|90° - B| = |A - B|

Since A is the larger angle, we can rewrite the equation as:

2|90° - B| = A - B

Now, let's consider two cases:

Case 1: B < 90°

In this case, 90° - B is positive. Therefore, we can rewrite the equation as:

2(90° - B) = A - B

Simplifying further:

180° - 2B = A - B

Combining like terms:

180° - B = A

Case 2: B > 90°

In this case, 90° - B is negative. Therefore, we can rewrite the equation as:

2(-(90° - B)) = A - B

Simplifying further:

-2(90° - B) = A - B

Expanding the equation:

-180° + 2B = A - B

Combining like terms:

-180° + 3B = A

In both cases, we have shown that A = 180° - B or A = -180° + 3B.

Therefore, we have proved that if A and B are adjacent angles, then 2|A-90°|=|a-b|.

Please note that the proof assumes that A and B are measured in degrees.