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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
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