Question

1. solve for x: (7x - 20)° (4x + 16)° 15) solve for x: (6x - 30)° 96°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. In the first problem, we set up the equation based on the equality of vertical angles: $7x - 20=4x + 16$.
$7x-4x=16 + 20$

Step2: Simplify the equation

Combining like - terms on both sides of the equation:
$3x=36$

Step3: Solve for x

Dividing both sides of the equation by 3:
$x = 12$

For the second problem:

Step1: Use the linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. So, we set up the equation $(6x - 30)+96=180$.
$6x-30=180 - 96$

Step2: Simplify the right - hand side

$6x-30 = 84$

Step3: Isolate the term with x

Adding 30 to both sides: $6x=84 + 30$
$6x=114$

Step4: Solve for x

Dividing both sides by 6: $x = 19$

Answer:

For the first problem, $x = 12$. For the second problem, $x = 19$.