Question

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

Explanation:

Step1: Find adjacent angle

The angle adjacent to \(105^\circ\) on the straight line is \(180^\circ - 105^\circ = 75^\circ\) (linear pair).

Step2: Use triangle angle sum

In a triangle, sum of angles is \(180^\circ\). Let the angles be \(72^\circ\), \(75^\circ\), and \(x\). So \(72^\circ + 75^\circ + x = 180^\circ\).

Step3: Solve for x

\(147^\circ + x = 180^\circ\), so \(x = 180^\circ - 147^\circ = 33^\circ\).

Answer:

33° (corresponding to the option with 33, likely the third option if options are ordered as given)