Question

solve for x. 106° 43° 63 149 31 43

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 $y$. Then $y+106^{\circ}+43^{\circ}=180^{\circ}$.

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

$y = 180^{\circ}-(106^{\circ}+43^{\circ})=180^{\circ}-149^{\circ}=31^{\circ}$.

Step3: Use the linear - pair property

The angle $x$ and the third - interior angle $y$ form a linear pair. A linear pair of angles sums to 180°. So $x + y=180^{\circ}$. Since $y = 31^{\circ}$, then $x=180^{\circ}-31^{\circ}=149^{\circ}$.

Answer:

149