Question

in the figure below, $\triangle ijk$ is drawn. the line $\overleftrightarrow{lim}$ is drawn such that $\overleftrightarrow{lim} \parallel \overline{jk}$.

$\text{m}\angle ijk = $ $\boldsymbol{\vee}$ because they are
$\boldsymbol{\vee}$

Explanation:

Step1: Recall Triangle Angle Sum

The sum of angles in a triangle is \(180^\circ\). In \(\triangle IJK\), we know two angles: \(\angle IJK = 47^\circ\) and \(\angle IKJ = 52^\circ\). Let \(\angle JIK = x^\circ\).

Step2: Calculate \(x\)

Using the triangle angle sum formula: \(47^\circ + 52^\circ + x^\circ = 180^\circ\).
First, sum the known angles: \(47 + 52 = 99\).
Then, solve for \(x\): \(x = 180 - 99 = 81\).

Answer:

\(81^\circ\) (Note: For the "because they are" part, it's about alternate interior angles or triangle angle sum. But the angle measure is \(81^\circ\).)