Question

find the value of x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(y\). So, \(y+37^{\circ}+84^{\circ}=180^{\circ}\).

Step2: Solve for \(y\)

\[

$$\begin{align*} y&=180^{\circ}-(37^{\circ} + 84^{\circ})\\ y&=180^{\circ}-121^{\circ}\\ y&=59^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

The angle \(x\) and \(y\) form a linear pair. A linear pair of angles sums to 180°. So, \(x + y=180^{\circ}\). Since \(y = 59^{\circ}\), then \(x=180^{\circ}-59^{\circ}\).

Answer:

\(x = 121\)