Question

find the value of x. the diagram is not to scale.
(diagram of a triangle with a 72° angle at the top, and an exterior angle of 105° at the bottom left, with the bottom right angle labeled x°)
options:
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, the sum of angles is \(180^\circ\). Let the unknown angle be \(x\). So, \(72^\circ + 75^\circ + x = 180^\circ\).

Step3: Solve for x

\(x = 180^\circ - 72^\circ - 75^\circ = 33^\circ\).

Answer:

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