Question

if $overline{eh}congoverline{gh}$, $mangle efh = 2x$, and $mangle gfh=x + 19^{circ}$, what is the value of $x? x=square^{circ}$

Explanation:

Step1: Apply congruent - triangle property

Since $\overline{EH}\cong\overline{GH}$ and $\angle E=\angle G = 90^{\circ}$, and $\overline{FH}=\overline{FH}$ (common side), by the Hypotenuse - Leg (HL) congruence criterion, $\triangle EFH\cong\triangle GFH$. Then $\angle EFH=\angle GFH$.

Step2: Set up the equation

Set $2x=x + 19$.

Step3: Solve the equation

Subtract $x$ from both sides: $2x−x=x + 19−x$. So $x = 19$.

Answer:

$19$