Question

find q.
write your answer as a whole number or a decimal. do not round.
q = yards

Explanation:

Step1: Identify similar triangles

Since \(\angle KJN=\angle LMN\), \(\angle KNJ = \angle LNM\) (vertical angles), by AA (Angle - Angle) similarity criterion, \(\triangle KNJ\sim\triangle LNM\).

Step2: Set up proportion

For similar triangles \(\triangle KNJ\) and \(\triangle LNM\), the ratios of corresponding sides are equal. So, \(\frac{q}{30}=\frac{75}{50}\).

Step3: Solve for \(q\)

Cross - multiply: \(50q=75\times30\). Then \(q=\frac{75\times30}{50}\). Calculate \(75\times30 = 2250\), and \(2250\div50=45\).

Answer:

\(45\)