Question

find ( mangle rsq ).
( mangle rsq=) (square^circ)

Explanation:

Step1: Identify the relationship between angles

We know that \( \angle RSJ = 90^{\circ}\) (right - angle) and \( \angle LSJ=36^{\circ}\). Also, \( \angle RSQ+\angle QSL+\angle LSJ = 180^{\circ}\), and \( \angle QSL=\angle PSQ\) (vertical angles are equal), and \( \angle PSR = 90^{\circ}\) (since \( \angle RSJ = 90^{\circ}\) and \( \angle PSJ = 180^{\circ}-\angle RSJ=90^{\circ}\)). Another way is to use the fact that \( \angle RSQ\) and \(36^{\circ}\) are complementary (because \( \angle RSJ = 90^{\circ}\)).

Step2: Calculate \(m\angle RSQ\)

Since \( \angle RSQ+\angle LSJ = 90^{\circ}\) (complementary angles, as \( \angle RSJ = 90^{\circ}\)), then \(m\angle RSQ=90^{\circ}-36^{\circ}\)

$$m\angle RSQ = 54^{\circ}$$

Answer:

\(54\)