The three Angles of a triangle are (x-25)degrees, (2x+40)degrees and 30 degrees. find the magnitude of each angle.
To find the magnitude of each angle in the given triangle, we need to set up and solve an equation based on the given information.
Let's assign variables to the angles of the triangle:
Angle 1: x-25 degrees
Angle 2: 2x+40 degrees
Angle 3: 30 degrees
According to the properties of a triangle, the sum of all angles in a triangle is always 180 degrees. Therefore, we can set up the following equation:
Angle 1 + Angle 2 + Angle 3 = 180 degrees
Substituting the variable expressions for the angles:
(x-25) + (2x+40) + 30 = 180
Now, we can solve this equation to find the value of x:
3x + 45 = 180
3x = 180 - 45
3x = 135
x = 135 / 3
x = 45
Once we have found the value of x, we can substitute it back into the expressions for each angle to find their magnitudes:
Angle 1: x - 25 = 45 - 25 = 20 degrees
Angle 2: 2x + 40 = 2(45) + 40 = 90 + 40 = 130 degrees
Angle 3: 30 degrees (given)
Therefore, the magnitudes of the angles in the triangle are:
Angle 1: 20 degrees
Angle 2: 130 degrees
Angle 3: 30 degrees