Find the 3 angles of the triangle

Question

A home has a triangle backyard. The second angle of this triangle is 6 degrees more than the first angle. The third angle is 2 degrees more than two times the first angle. find the angles of the triangular yard. 

Answer 1

Jeremy,

 

Label the 3 corners of your triangle a, b, and c, with the 1st angle being a, 2nd b and 3rd c.

 

Then  with the 1st angle = a,

 

2nd angle b = (a + 6°)

 

and 3rd angle c = (2·a + 2°)

 

Now for any triangle the sum of the three angles a + b + c = 180°

 

Substituting we get:  a + (a + 6°) + (2·a + 2°) = 180°

 

Simplifying:  4·a + 8° = 180°, so 4·a = 172° and 

 

a = 43°

b = 49°

c = 88°

 

If you check, you will see that these three angle sum to 180° as they should.