Question

The figure shows two intersecting lines and measures of the resulting angles write an equation to help you solve for x , then fine the value of x.

Answer 1

Given:

Given that two lines are intersecting at the point.

The angles (3x - 8)° and (2x + 12)° are the angles formed by the intersection of the two lines.

We need to determine the equation to solve for x and the value of x.

Equation:

The two angles (3x - 8)° and (2x + 12)° are vertically opposite. Hence, the vertically opposite angles are always equal.

Hence, we have;

`3x-8=2x+12`

Hence, the equation is
`3x-8=2x+12`

Value of x:

The value of x can be determined by solving the equation
`3x-8=2x+12`

Thus, we have;

`3x-8=2x+12`

Subtracting both sides of the equation by 2x, we get;

`x-8=12`

Adding both sides of the equation by 8, we get;

`x=20`

Thus, the value of x is 20.

Hence, the equation and the value of x are
`3 x-8=2 x+12 \ and\ x=20`

Thus, Option D is the correct answer.