Question

find q. 51 m 33 m q 68 m

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle IKJ\) and \( \triangle MLJ\) are similar. Because \( \angle IKJ=\angle MLJ\), \( \angle KIJ = \angle LMJ\) (given equal angles), and \( \angle IJK=\angle MJL\) (vertically - opposite angles).

Step2: Set up the proportion

By the property of similar triangles (corresponding sides are in proportion), we have \(\frac{IK}{ML}=\frac{KJ}{LJ}\). Let \(IK = 51\), \(ML=68\), \(KJ = 33\), and \(LJ=q\). Then \(\frac{51}{68}=\frac{33}{q}\).

Step3: Cross - multiply

Cross - multiplying gives \(51q=33\times68\).

Step4: Solve for \(q\)

First, calculate \(33\times68 = 2244\). Then \(q=\frac{2244}{51}\). Since \(2244\div51 = 44\).

Answer:

\(44\) m