Question

find the value of x. 38° 96° x° x =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(y\). So, \(y+38^{\circ}+96^{\circ}=180^{\circ}\).

Step2: Solve for \(y\)

\[

$$\begin{align*} y&=180^{\circ}-(38^{\circ} + 96^{\circ})\\ y&=180^{\circ}-134^{\circ}\\ y& = 46^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

The angle \(x\) and \(y\) form a linear pair. Since the sum of angles in a linear pair is 180°, \(x + y=180^{\circ}\). Substitute \(y = 46^{\circ}\) into the equation: \(x=180^{\circ}-y\).

Step4: Calculate \(x\)

\[

$$\begin{align*} x&=180^{\circ}-46^{\circ}\\ x&=134^{\circ} \end{align*}$$

\]

Answer:

\(134\)