Question

The figure shows two intersecting lines and the measures of the resulting angles. Write an equation to help you solve for x. Then find the value of x.

Answer 1

Given:

The given figure shows the intersection of the two lines.

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

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

Equation to solve for x:

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

Hence, we have;

$3x-8=2x+12$

Thus, the equation to solve for x 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;

$x-8=12$

     $x=20$

Thus, the value of x is 20.