The angles of the triangle are proportional to the numbers 3.8.5. Prove that this triangle is right-angled.

Let the angle, which is the smallest of all, be equal to the variable 3m.

Then, in accordance with the conditions, the average angle can be represented as 5m.

Therefore, the angle that is the largest can be expressed in terms of 8m.

Since we know that these are all the angles of a triangle, we are able to write down the equation and find out what value the largest angle will correspond to:

3m + 5m + 8m = 180;

16m = 180;

m = 11.25;

11.25 * 8 = 90.

Answer: The largest angle is 90 °, which means a rectangular triangle.




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