The first angle of a triangle is twice the second and the third is 5 degrees larger than the first. Find the 3 angles?
The three angles of this triangle are 35 degrees, 70 degrees, and 75 degrees, respectively. Here is how to figure that out:
Let us call the first angle A, the second B and the third C. That gives us the equations:
A = 2B and C = A + 5
We also know that the sum of the angles of a triangle equal 180 degrees. Therefore
A + B + C = 180
Substituting in for A and C we get
2B + B + 2B + 5 = 180
5B = 175
B = 35
That allows us to see that
A = 70 and C = 75
Let's consider the values of the 3 angles:
x = the value in degrees, of the smallest angle, wich is the second angle;
2x = the value in degrees, of the second angle;
2x+5 = the value in degree, of the 3rd angle.
We know also that the sum of the angles in a triangle is 180 degrees.
x+2x+2x+5 = 180
Let the second angle be x .
Then by data 1st angle = 2x
3rd angle = 1st angle +5 = 2x+5.
Sumo the 3 angles (algebraic) = 2x + x + (2x+5) should be equal to 180 degree.
5x+5 =180. Or
5x = 180-5 = 175 So
x = 175/5 = 35 degree is the 2nd angle.
Therefore the 1st angle = 2x =2*35 = 70 deg.
#rd angle = 2x+5 = 70 +5 = 75.