Question

what is the value of x? x - 44°

Explanation:

Step1: Recall circle - angle property

The angle inscribed in a semi - circle is a right angle. So, triangle $IGH$ is a right - triangle with $\angle IHG = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle IGH$, the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle I=x - 44^{\circ}$, $\angle H = 90^{\circ}$, and $\angle G$ be an acute angle. We know that $\angle I+\angle H+\angle G=180^{\circ}$. In a right - triangle, if we assume the non - right angles are complementary (since $\angle G + \angle I=90^{\circ}$). We have the equation $x-44^{\circ}+90^{\circ}=90^{\circ}$ (because the non - right angles in a right - triangle add up to 90 degrees).

Step3: Solve the equation for $x$

$x-44^{\circ}=0^{\circ}$. Add $44^{\circ}$ to both sides of the equation: $x=44^{\circ}$.

Answer:

$44$