Question

How do I figure this out?

Answer 1

a = 9

Explanation:

Since QS is an angle bisector then the following ratios are equal

`(QP)/(QR)` =
`(PS)/(RS)`

[ note that SR = 24 - a ]

substituting values into the equation

`(15)/(25)` =
`(a)/(24-a)` ( cross- multiply )

25a = 15(24 - a)

25a = 360 - 15a ( add 15a to both sides )

40a = 360 ( divide both sides by 40 )

a = 9