Question

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

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle of \(105^{\circ}\) is \(180 - 105=75^{\circ}\) (linear - pair angles).

Step2: Use the triangle - angle - sum theorem

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the three angles of the triangle be \(72^{\circ}\), \(75^{\circ}\), and \(x^{\circ}\). Then \(72 + 75+x=180\).
Simplify the left - hand side: \(147+x = 180\).
Subtract \(147\) from both sides: \(x=180 - 147\).

Answer:

\(33\)