Question

a mechanic is constructing the metal structure shown.
both \\(\overline{fj}\\) and \\(\overline{ik}\\) measure 4 m and are perpendicular to \\(\overline{gh}\\). the measure of \\(\angle kih = 40^\circ\\) and \\(\overline{gj} \cong \overline{hk}\\).
what is the measure of \\(\angle fgj\\)?
\\(\bigcirc\\) a. \\(20^\circ\\)
\\(\bigcirc\\) b. \\(40^\circ\\)
\\(\bigcirc\\) c. \\(50^\circ\\)
\\(\bigcirc\\) d. \\(90^\circ\\)

Explanation:

Step1: Identify right triangles

$\triangle FJG$ and $\triangle IKH$ are right triangles (since $\overline{FJ} \perp \overline{GH}$, $\overline{IK} \perp \overline{GH}$).

Step2: Match congruent triangle parts

$\overline{FJ} = \overline{IK} = 4\ \text{m}$, $\overline{GJ} \cong \overline{HK}$, so $\triangle FJG \cong \triangle IKH$ (SAS congruence).

Step3: Corresponding angles are equal

Corresponding angles of congruent triangles are equal, so $\angle FGJ = \angle KIH$.

Step4: Substitute given angle value

$\angle KIH = 40^\circ$, so $\angle FGJ = 40^\circ$.

Answer:

B. $40^\circ$