The three angles of a triangle are (x-25) degrees, (2x+40)degrees and 30 degrees. find the magnitude of each angle.
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?
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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