# 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?

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### 3 Answers

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.

(ii)

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