Question

Solve for x in the following triangle.​

Answer 1

x = 12

Explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

8 + 6x is an exterior angle of the triangle, thus

8 + 6x = 30 + 4x + 2 = 4x + 32 ( subtract 4x from both sides )

8 + 2x = 32 ( subtract 8 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Answer 2

The solution to the equation is x equals 12, representing the value that satisfies the relationship between the exterior and interior angles of the triangle.

The given equation,

8+6x=30+4x+2,

represents the relationship between an exterior angle (8 + 6x) of a triangle and the sum of its two opposite interior angles (30 + 4x + 2). To solve for x, one subtracts 4x from both sides, yielding

8+2x=32

Subtracting 8 from both sides further simplifies the equation to

2x=24

Finally, dividing both sides by 2 gives

x=12.