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, $y+46^{\circ}+97^{\circ}=180^{\circ}$.

Step2: Solve for the third - interior angle $y$

$y = 180^{\circ}-(46^{\circ}+97^{\circ})=180^{\circ}-143^{\circ}=37^{\circ}$.

Step3: Use the linear - pair property

The angle $x$ and the third - interior angle $y$ form a linear pair. Since the sum of angles in a linear pair is 180°, we have $x + y=180^{\circ}$. Substituting $y = 37^{\circ}$, we get $x=180^{\circ}-37^{\circ}$.

Answer:

$143$