Given:
ST || RU
To find:
The measure of QS.
Solution:
In triangle QRU and QST,
[tex]\angle RQU\cong \angle SQT[/tex] [Common angle]
[tex]\angle QRU\cong \angle QST[/tex] [Corresponding angle]
[tex]\triangle RQU\sim \triangle SQT[/tex] [AA property of similarity]
The corresponding sides of similar triangles are proportional.
[tex]\dfrac{QR}{QS}=\dfrac{QU}{QT}[/tex]
[tex]\dfrac{23}{QS}=\dfrac{25}{25+50}[/tex]
[tex]\dfrac{23}{QS}=\dfrac{25}{75}[/tex]
[tex]\dfrac{23}{QS}=\dfrac{1}{3}[/tex]
On cross multiplication, we get
[tex]3(23)=1(QS)[/tex]
[tex]69=QS[/tex]
Therefore, the measure of QS is 69.
