Answer:
a = 9
Step-by-step explanation:
Since QS is an angle bisector then the following ratios are equal
[tex]\frac{QP}{QR}[/tex] = [tex]\frac{PS}{RS}[/tex]
[ note that SR = 24 - a ]
substituting values into the equation
[tex]\frac{15}{25}[/tex] = [tex]\frac{a}{24-a}[/tex] ( cross- multiply )
25a = 15(24 - a)
25a = 360 - 15a ( add 15a to both sides )
40a = 360 ( divide both sides by 40 )
a = 9
