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The angles of triangle are 3x, (2x 10) and(5x- 40). Find the angles. Hence show that the triangle is an equilateral triangle.?
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The angles of triangle are 3x, (2x 10) and(5x- 40). Find the angles. H...
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The angles of triangle are 3x, (2x 10) and(5x- 40). Find the angles. H...
Solution:


Given, the angles of a triangle are 3x, (2x + 10) and (5x - 40).

We know that the sum of all angles of a triangle is 180°. Therefore, we can write:

3x + (2x + 10) + (5x - 40) = 180°

Simplifying the above equation, we get:

10x - 30 = 180°

10x = 210°

x = 21°

Therefore, the angles of the triangle are:

3x = 3(21°) = 63°

2x + 10 = 2(21°) + 10 = 52°

5x - 40 = 5(21°) - 40 = 55°

Now, to show that the triangle is an equilateral triangle, we need to prove that all the angles are equal.

Let's check:

63° = 63°

52° = 52°

55° = 55°

As all the angles are equal, we can say that the triangle is an equilateral triangle.

Therefore, the angles of the given triangle are 63°, 52°, and 55°, and it is an equilateral triangle.
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The angles of triangle are 3x, (2x 10) and(5x- 40). Find the angles. Hence show that the triangle is an equilateral triangle.?
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