Question

find the value of x. the diagram is not to scale. 72° 105° x° 147 33 75 162

Explanation:

Step1: Find adjacent - interior angle

The adjacent - interior angle to the $105^{\circ}$ exterior angle is $180 - 105=75^{\circ}$ since they are a linear pair.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let the three interior angles of the triangle be $72^{\circ}$, $75^{\circ}$, and $x^{\circ}$. So, $72 + 75+x=180$.

Step3: Solve for $x$

$x=180-(72 + 75)=180 - 147 = 33$.

Answer:

33