Question

∠1≅∠2 m∠1 = x - 5

Explanation:

Step1: Use angle - sum property

The sum of the three angles is 180 degrees. Since $\angle1\cong\angle2$ and $m\angle1 = x - 5$, $m\angle2=x - 5$, and the third - angle is 90 degrees. So, $(x - 5)+(x - 5)+90=180$.

Step2: Simplify the left - hand side

Combine like terms: $2(x - 5)+90=180$. Expand $2(x - 5)$ to get $2x-10 + 90=180$, then $2x+80 = 180$.

Step3: Isolate the variable term

Subtract 80 from both sides: $2x+80-80=180 - 80$, which gives $2x=100$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{100}{2}$, so $x = 50$.

Answer:

$x = 50$