Question

Call has a triangular backyard. The second angle of the triangle is 6° more than the first angle, and the third angle is 9° more than three times the first angle. Find the angles of the triangular yard.

Answer 1

The angles of the triangular backyard are 33°, 39°, and 108°.

Step-by-step explanation:

Let's represent the three angles of the triangular backyard as 'x', 'x + 6°', and '3x + 9°'. According to the properties of a triangle, the sum of the three angles is 180°. So, we can write the equation:

x + (x + 6°) + (3x + 9°) = 180°

Simplifying the equation, we have:

5x + 15° = 180°

Subtracting 15° from both sides, we get:

5x = 165°

Dividing both sides by 5, we find:

x = 33°

Now, substituting the value of 'x' back into the angles, we can find the values of the other two angles:

First angle: 33°

Second angle: 33° + 6° = 39°

Third angle: 3(33°) + 9° = 108°