Question

A home has a triangular backyard. The second angle of the triangle is 4degrees more than the first angle. The third angle is 8degrees more than two times the first angle. Find the angles of the triangular yard.
The measure of the first angle is

Answer 1

Let $x$ be the first angle.

"The second angle of the triangle is 4 degrees more than the first angle" means that the second angle is $x+4$

"The third angle is 8 degrees more than two times the first angle" means that the third angle is $2x+8$

So, on the one hand, the sum of the angles of the triangle is

$x+(x+4)+(2x+8) = 4x+12$

On the other hand, the sum of the sides of any triangle is 180 degrees. So, we have

$4x+12=180 \iff 4x = 168 \iff x = 42$

Answer 2

Answer:

1st angle = X

2nd angle = X + 7

3rd angle = X + 18

Then (sum. them): 3X + 25 = 180   ==>  X = 51.67 degree

Therefore,

1st angle = 51.67 degree

2nd angle = 58.67 degree

3rd angle = 69.67 degree