# The first angle of a triangle is twice the second and the third is 5 degrees larger than the first. Find the 3 angles?

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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

5x+5= 180

5x=175

x=35 degrees

2x=2*35

2x=70 degrees

2x+5=70+5=75 degrees

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.

Or

2x+x+2x+5 =180.

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.