Question

if (mangle abj = 28^{circ},angle abccongangle dbj,) find (mangle jbc).

Explanation:

Step1: Recall angle - relationship

Since $\angle ABC\cong\angle DBJ$ and $\angle ABJ = 28^{\circ}$, assume $\angle ABC=\angle DBJ = x$. Also, note that $\angle ABJ+\angle JBC+\angle ABC = 90^{\circ}$ (from the right - angle symbol in the figure).

Step2: Set up the equation

We know that $\angle ABJ = 28^{\circ}$, and $\angle ABJ+\angle JBC+\angle ABC = 90^{\circ}$. Since $\angle ABC=\angle DBJ$, and let $\angle ABC = y$. We have $28^{\circ}+\angle JBC + y=90^{\circ}$. Also, because of the congruence, we can consider the fact that the non - overlapping parts of the right - angles are related. In this case, $\angle JBC=90^{\circ}-\angle ABJ$.

Step3: Calculate the angle

Substitute $\angle ABJ = 28^{\circ}$ into the formula $\angle JBC=90^{\circ}-\angle ABJ$. So, $\angle JBC = 90 - 28=62^{\circ}$.

Answer:

$62^{\circ}$