Question

what is the value of x?
x + 28°
h
g
f
x = °

Explanation:

Step1: Recognize isosceles - triangle

Since $FG = HG$, $\triangle FHG$ is an isosceles triangle. So, $\angle HFG=\angle FHG=x + 28^{\circ}$.

Step2: Use angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$. In $\triangle FHG$, we have $\angle HFG+\angle FHG+\angle FGH = 180^{\circ}$. And since the angle inscribed in a semi - circle is a right angle, $\angle FGH = 90^{\circ}$. So, $(x + 28^{\circ})+(x + 28^{\circ})+90^{\circ}=180^{\circ}$.

Step3: Simplify the equation

$2x+28^{\circ}+28^{\circ}+90^{\circ}=180^{\circ}$, $2x+146^{\circ}=180^{\circ}$.

Step4: Solve for $x$

Subtract $146^{\circ}$ from both sides: $2x=180^{\circ}-146^{\circ}=34^{\circ}$. Then divide both sides by 2: $x = 17^{\circ}$.

Answer:

$17$