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ANSWER

[tex] m∠RQS =36 \degree[/tex]


EXPLANATION

From the diagram, m∠PQR and m∠RQS are complementary.


This means that the two angles will add up to 90°.


[tex]m∠PQR + m∠RQS = 90 \degree...(1)[/tex]




Also, we were given that,


[tex]m∠PQR: m∠RQS = 3:2[/tex]

[tex] \frac{m∠PQR}{m∠RQS } = \frac{3}{2} [/tex]


This implies that,


[tex]m∠PQR= \frac{3}{2} m∠RQS ....(2)[/tex]

We put equation (2) into equation (1) to get,


[tex]\frac{3}{2} m∠PQS + m∠RQS = 90 \degree[/tex]


Multiply through by 2 to get,



[tex]3m∠PQS +2 m∠RQS =180 \degree[/tex]

[tex]5 m∠RQS =180 \degree[/tex]


Divide through by 5.



[tex] m∠RQS =36 \degree[/tex]

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