Answer:
x = 25
Step-by-step explanation:
It is given that, ray Ray AP bisects angle CAT. It means,
[tex]\angle CAT=\angle CAP+\angle PAT[/tex]
Also, [tex]\angle CAP = \angle PAT[/tex]
It gives, [tex]\angle CAT=2\angle PAT[/tex]
ATQ,
[tex]\angle CAT = 5x+17 \ \text{and}\ \text{PAT}=3x-4[/tex]
So,
[tex]5x+17=2(3x-4)\\\\5x+17=6x-8[/tex]
Taking like terms together,
[tex]5x-6x=-8-17\\\\-x=-25\\\\x=25[/tex]
So, the value of x is 25.
