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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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

 

 

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