Question

if (mangle ihj) is (42^{circ}), what is (mangle ijh?
45^{circ}
48^{circ}
138^{circ}
228^{circ})

Explanation:

Step1: Recall angle - sum property of a right - triangle

Assume that $\angle IJH$ and $\angle IHJ$ are in a right - triangle (since the problem is likely related to circle - inscribed right - triangles, where an inscribed angle subtended by a diameter is a right angle). The sum of the interior angles of a triangle is $180^{\circ}$, and if one of the angles is $90^{\circ}$, then for a triangle $\triangle IJH$ with $\angle IHJ = 42^{\circ}$ and $\angle JIH=90^{\circ}$, we use the formula $\angle IJH+\angle IHJ+\angle JIH = 180^{\circ}$.

Step2: Solve for $\angle IJH$

We can rewrite the formula as $\angle IJH=180^{\circ}-\angle IHJ - \angle JIH$. Substituting $\angle IHJ = 42^{\circ}$ and $\angle JIH = 90^{\circ}$, we get $\angle IJH=180^{\circ}-90^{\circ}-42^{\circ}=48^{\circ}$.

Answer:

B. $48^{\circ}$