Question

С
0
A
(3x + 13)
(x-8)
в

Answer 1

In triangle ABC, where angles A, B, and C are represented by expressions in terms of x, the solution is x = 35. The sum of the interior angles (A, B, and C) in a triangle equals 180 degrees.

In a triangle, the sum of all three interior angles is always equal to 180 degrees. Therefore, in triangle ABC:

`\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]`

Given:

`\[ \text{Angle A} = 3x + 13 \]`

`\[ \text{Angle B} = x - 8 \]`

`\[ \text{Angle C} = x \]`

Substitute these values into the equation:

`\[ (3x + 13) + (x - 8) + x = 180 \]`

Combine like terms:

5x + 5 = 180

Subtract 5 from both sides:

5x = 175

Divide by 5:

x = 35

Therefore, x = 35.