Question

PLEASE HELPP!!!!! WILL GIVE BRAINLIEST

Answer 1

ANSWER

$m∠RQS =36 \degree$


EXPLANATION

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


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


$m∠PQR + m∠RQS = 90 \degree...(1)$




Also, we were given that,


$m∠PQR: m∠RQS = 3:2$

$\frac{m∠PQR}{m∠RQS } = \frac{3}{2}$


This implies that,


$m∠PQR= \frac{3}{2} m∠RQS ....(2)$

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


$\frac{3}{2} m∠PQS + m∠RQS = 90 \degree$


Multiply through by 2 to get,



$3m∠PQS +2 m∠RQS =180 \degree$

$5 m∠RQS =180 \degree$


Divide through by 5.



$m∠RQS =36 \degree$