Question

what is the value of x? 32 71 109 90

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be $y$. So, $y+64^{\circ}+45^{\circ}=180^{\circ}$.

Step2: Calculate the third - interior angle

$y = 180^{\circ}-(64^{\circ}+45^{\circ})=180^{\circ}-109^{\circ}=71^{\circ}$.

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 $y = 71^{\circ}$, we get $x=180^{\circ}-71^{\circ}=109^{\circ}$.

Answer:

109