Question

1. ray o is perpendicular to line p in the diagram shown. determine the value of x. show or explain your thinking.

Explanation:

Step1: Define total right angle

Perpendicular lines form $90^\circ$.

Step2: Set up angle equation

Sum of angles equals $90^\circ$:
$30^\circ + 3x = 90^\circ$

Step3: Isolate the variable term

Subtract $30^\circ$ from both sides:
$3x = 90^\circ - 30^\circ$
$3x = 60^\circ$

Step4: Solve for $x$

Divide both sides by 3:
$x = \frac{60^\circ}{3}$

Answer:

$x = 20^\circ$