Question

find the longest side of \\( \triangle i j k \\).

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((a + 71)+14a+(a + 61)=180\).

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Step2: Calculate each angle

• \(\angle I=a + 71=3+71 = 74^{\circ}\)
• \(\angle J=14a=14\times3 = 42^{\circ}\)
• \(\angle K=a + 61=3+61 = 64^{\circ}\)

Step3: Relate angles and sides

In a triangle, the larger the angle, the longer the side opposite it. Since \(\angle I = 74^{\circ}\) is the largest angle, the side opposite \(\angle I\) (which is \(JK\)) is the longest side.

Answer:

\(JK\)