Question

in the figure below, $\triangle fgh$ is drawn. the line $\overleftrightarrow{ifj}$ is drawn such that $\overleftrightarrow{ifj} \parallel \overline{gh}$.
$\text{m}\angle fgh = \quad$ because they are

Explanation:

Step1: Find the third angle in triangle FGH

The sum of angles in a triangle is \( 180^\circ \). In \( \triangle FGH \), we know \( \angle FGH = 57^\circ \) and \( \angle FHG = 43^\circ \). Let \( \angle GFH = y \). Then:

$$ y + 57^\circ + 43^\circ = 180^\circ $$

$$ y + 100^\circ = 180^\circ $$

$$ y = 180^\circ - 100^\circ = 80^\circ $$

Step2: Use the property of parallel lines (supplementary angles)

Since \( \overleftrightarrow{IFJ} \parallel \overline{GH} \), \( \angle GFH \) and \( x^\circ \) are supplementary (they form a linear pair). So:

$$ x + y = 180^\circ $$

We know \( y = 80^\circ \), so:

$$ x + 80^\circ = 180^\circ $$

$$ x = 180^\circ - 80^\circ = 100^\circ $$

Answer:

\( x = 100 \)