Which are the 3 angles of the triangle if the second angle is 20 degrees greater than the first and the 3rd angle is twice than the second?
The answer is that the first angle is 30 degrees, the second is 50 degrees, and the third is 100 degrees.
Let's call the angles A, B and C.
We know that
A + B + C = 180 because that's how many degrees are in the three angles of a triangle.
We know that B = 20 + A and we know that C = 2B
So that gets us the equation
A + 20 + A + (2(20+a)) = 180
2A + 40 + 2A = 160
4A = 120
A = 30
B = A + 20
B = 30 + 20
B = 50
C = 2B
C = 2*50
C = 100
Let's consider the values of the 3 angles:
x = the value in degrees, of the first angle;
y = the value in degrees, of the second angle;
z = the value in degree, of the third angle.
The equation which express the constraint from enunciation that the second angle is 20 degrees greater than the first angle, is:
y = x+20, so x = y-20
The third angle is twice than the second.
z = 2y
We know also that the sum of the angles in a triangle is 180 degrees.
x+y+z = 180
We'll write each unknown depending on the second angle, y:
y-20 + y + 2y = 180
4y = 180+20
4y = 200
y = 50 degrees
So, the first angle will have:
x = y-20
x = 50-20
y = 30 degrees
The third angle is :
z = 2y
z = 2*50
z = 100 degrees.
Let the 1st angle be x degrees.. then the the secod angle by data is x +20 degrees . The 3rd angle by data is twice 2nd implies the angle is (i) 2(x+20). (ii) But twice more than second implies it is (x+20)+2(x+20) = 3(x+20).
So sum of 3 angles of the triangle =(x)+ (x+20)+2(x+20) shuld be equal to 180 deg.
Or 4x+60 = 180 Or
4x = 180-60 = 120. Or x = 120/4 = 30 degrees. So the angles are 30 deg, (30+20) =50 deg and 2*50 = 100 deg.
If you mean the 2d angle is twice geater than second impling x+20+2(x+20) = 3x+20. Then the sum 3 angle of the triangle are x+(x+20)+(3x+60) should be equal to 180 degrees.. Or
5x+80 = 180. Or
5x= 180-80 =100. Or
x = 100/5 = 20 degrees.
So the angles of the triangle are:
x= 20 deg
x+20 = 40 and
x+20+2(x+20) = 3x+60 = 3*20+60 =120 deg