Question

find the largest angle of \\(\triangle ijk\\). assume that \\(z\\) is a positive number.

Explanation:

Step1: Compare side lengths

Since \( z>0 \), \( 115z > 46z \), so \( IJ > KJ \).

Step2: Relate sides to angles

In a triangle, longer sides face larger angles. So \( \angle K > \angle I \).

Step3: Analyze given angle

We know \( \angle J = 95^\circ \), which is greater than \( 90^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle I + \angle K = 180^\circ - 95^\circ = 85^\circ \). This means both \( \angle I \) and \( \angle K \) are less than \( 95^\circ \).

Answer:

\(\angle J\)