Question

if $overline{gh}congoverline{gj}$, $mangle{gih}=s + 26^{circ}$, and $mangle{gij}=3s$, what is the value of $s? s=square^{circ}$

Explanation:

Step1: Identify congruent - angle relationship

Since $\overline{GH}\cong\overline{GJ}$ and $\angle IJG = \angle IHG=90^{\circ}$, and $\overline{IG}=\overline{IG}$ (common side), by the Hypotenuse - Leg (HL) congruence theorem, $\triangle IJG\cong\triangle IHG$. Then $\angle GIH=\angle GIJ$.

Step2: Set up the equation

We know that $m\angle GIH = s + 26^{\circ}$ and $m\angle GIJ = 3s$. So we set up the equation $s + 26=3s$.

Step3: Solve the equation

Subtract $s$ from both sides: $26=3s - s$.
Simplify the right - hand side: $26 = 2s$.
Divide both sides by 2: $s = 13$.

Answer:

$13$