Question

question in △ijk, jk = 19, ki = 16, and ij = 5. which statement about the angles of △ijk must be true? answer m∠i > m∠k > m∠j m∠i > m∠j > m∠k m∠k > m∠j > m∠i m∠j > m∠k > m∠i m∠j > m∠i > m∠k m∠k > m∠i > m∠j

Explanation:

Step1: Recall angle - side relationship

In a triangle, the larger the side length opposite an angle, the larger the measure of the angle.

Step2: Identify side - angle pairs

In \(\triangle IJK\), side \(JK\) is opposite \(\angle I\), \(KI\) is opposite \(\angle J\), and \(IJ\) is opposite \(\angle K\). Given \(JK = 19\), \(KI=16\), and \(IJ = 5\).

Step3: Compare side lengths

We have \(JK>KI>IJ\).

Step4: Determine angle - size order

Since the side opposite \(\angle I\) is the longest (\(JK\)), the side opposite \(\angle J\) is the second - longest (\(KI\)), and the side opposite \(\angle K\) is the shortest (\(IJ\)), we have \(m\angle I>m\angle J>m\angle K\).

Answer:

\(m\angle I > m\angle J > m\angle K\) (the option corresponding to this in the multiple - choice list)