Question

find the value of x.

Explanation:

Step1: Find the adjacent angle to 146°

The angle adjacent to \(146^\circ\) on a straight line is \(180^\circ - 146^\circ = 34^\circ\).

Step2: Use triangle angle sum property

The sum of angles in a triangle is \(180^\circ\). So, \(x + 40^\circ + 34^\circ = 180^\circ\).
Simplify: \(x + 74^\circ = 180^\circ\).
Subtract \(74^\circ\) from both sides: \(x = 180^\circ - 74^\circ = 106^\circ\).

Answer:

\(x = 106^\circ\)