Isosceles and Equilateral Triangles | CK-12 Foundation - Free Printable

Let’s solve this step by step.

We are given a triangle with three angles expressed in terms of x:

- One angle is (5x - 1)°
- Another angle is (8x + 5)°
- The third angle is (4x + 6)°

In any triangle, the sum of all interior angles is always 180 degrees.

So we can write an equation:

(5x - 1) + (8x + 5) + (4x + 6) = 180

Now let’s combine like terms.

First, add up all the x terms:

5x + 8x + 4x = 17x

Now add up the constant numbers:

-1 + 5 + 6 = 10

So our equation becomes:

17x + 10 = 180

Now subtract 10 from both sides:

17x = 170

Now divide both sides by 17:

x = 10

✔ Let’s check if this works.

Plug x = 10 into each angle:

- First angle: 5(10) - 1 = 50 - 1 = 49°
- Second angle: 8(10) + 5 = 80 + 5 = 85°
- Third angle: 4(10) + 6 = 40 + 6 = 46°

Add them: 49 + 85 + 46 = 180 → ✔️ Correct!

Final Answer:
x = 10