Question

Один із зовнішніх кутів трикутника дорівнює 125° а один із кутів трикутника не суміжний з ним 81° знайти невідомі внутрішні кути трикутника

Answer 1

Ответ:55,81,44

Объяснение180-125=55,

55+81=136

180-136=44

Answer 2

Finding the Unknown Interior Angles of a Triangle

To find the unknown interior angles of a triangle, we can use the fact that the sum of all interior angles in a triangle is always 180 degrees.

Let's denote the three interior angles of the triangle as A, B, and C. We are given that one of the exterior angles of the triangle is 125 degrees, and one of the angles is not adjacent to it and measures 81 degrees.

We know that the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, we can find the measure of the adjacent interior angle by subtracting the given exterior angle from 180 degrees.

Let's denote the exterior angle as X and the adjacent interior angle as Y. We have:

X + Y = 180 degrees

Given that X = 125 degrees, we can substitute this value into the equation:

125 + Y = 180

Now, we can solve for Y:

Y = 180 - 125 Y = 55 degrees

So, one of the interior angles adjacent to the 125-degree exterior angle measures 55 degrees.

Now, we can find the remaining interior angle by subtracting the sum of the two known interior angles from 180 degrees:

A + B + C = 180 degrees

Given that A = 125 degrees and B = 55 degrees, we can substitute these values into the equation:

125 + 55 + C = 180

Now, we can solve for C:

C = 180 - 125 - 55 C = 180 - 180 C = 0 degrees

Therefore, the remaining interior angle, which is not adjacent to the 125-degree exterior angle, measures 0 degrees.

To summarize, the unknown interior angles of the triangle are as follows: - One interior angle adjacent to the 125-degree exterior angle measures 55 degrees. - The remaining interior angle, which is not adjacent to the 125-degree exterior angle, measures 0 degrees.

Please note that the sum of the interior angles of a triangle should always be 180 degrees. In this case, the sum of the three interior angles is 55 + 0 + 125 = 180 degrees, confirming the validity of our calculations.

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