The three angles of a triangle are (x-25) degrees, (2x+40)degrees and 30 degrees. find the magnitude of each angle.
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Well, let's solve this triangle puzzle!
The sum of the three angles in a triangle is always 180 degrees. So, we can set up an equation:
(x-25) + (2x+40) + 30 = 180
Simplifying the equation gives us:
3x + 45 = 180
Subtracting 45 from both sides:
3x = 135
Dividing both sides by 3:
x = 45
Now that we know x, we can substitute it back into the expressions for the angles:
First angle: (x-25) = (45-25) = 20 degrees
Second angle: (2x+40) = (2*45 + 40) = 130 degrees
Third angle: 30 degrees (given)
So, the magnitude of each angle is:
Angle 1: 20 degrees
Angle 2: 130 degrees
Angle 3: 30 degrees
And there you have it! A triumphant trio of angle magnitudes!
To find the magnitude of each angle in a triangle, we need to set up an equation using the fact that the sum of all angles in a triangle is always 180 degrees.
Given the three angles of the triangle: (x-25), (2x+40), and 30 degrees, we can write the equation:
(x-25) + (2x+40) + 30 = 180
Now, let's solve this equation to find the value of x.
Combine like terms:
3x + 45 = 180
Subtract 45 from both sides:
3x = 135
Divide both sides by 3:
x = 45
Now that we know x = 45, we can substitute this value back into the expressions for each angle to find their magnitudes.
First angle: (x-25) = (45-25) = 20 degrees
Second angle: (2x+40) = (2*45+40) = 130 degrees
Third angle: 30 degrees (already given)
Therefore, the magnitude of each angle in the triangle is:
1st angle = 20 degrees
2nd angle = 130 degrees
3rd angle = 30 degrees
This an easy deal when recalling the fundamental identity for traingles, namely that the sum of the three angles must be identically 180 degrees. (Why precisely 180°?)
This means:
(x-25) + (2x+40) + 30 = 180
This can be simplified to:
3x + 45 = 180
Subtracting 45 on both sides yields:
3x = 135
Multiplying this 1/3-times, one immediately finds:
x=45
It is not neceassry but quite useful to substitute the obtained value directly back into the aforementioned equation in order to verify this as the solution.
Question to think further: Why is there just one solution?