Question

Find the value of X that makes the drawing below true (drawing is not to scale)

Answer 1

Given:

Given that the angles (12y + 5)° and (18y - 7)° are vertical angles.

Also, given the other angle is (3x + 1)°

We need to determine the value of x.

Value of y:

Since, the angles (12y + 5)° and (18y - 7)° are vertical angles, then they must be congruent.

Thus, we have;

$12y+5=18y-7$

$-6y+5=-7$

      $-6y=-12$

          $y=2$

Thus, the value of y is 2.

Value of x:

From the figure, it is obvious that the angles (18y - 7)° and (3x + 1)° are linear pairs.

Thus, we have;

$18y-7+3x+1=180$

Substituting y = 2, we get;

$36-7+3x+1=180$

            $3x+30=180$

                    $3x=150$

                     $x=50$

Thus, the value of x is 50.