Question

It is known that Ray AP bisects angle CAT. If m<CAT = 5x+17 and m<PAT = 3x-4, then determine the value of x.​

Answer 1

x = 25

Explanation:

It is given that, ray Ray AP bisects angle CAT. It means,

`\angle CAT=\angle CAP+\angle PAT`

Also,
`\angle CAP = \angle PAT`

It gives,
`\angle CAT=2\angle PAT`

ATQ,

`\angle CAT = 5x+17 \ \text{and}\ \text{PAT}=3x-4`

So,

`5x+17=2(3x-4)\\\\5x+17=6x-8`

Taking like terms together,

`5x-6x=-8-17\\\\-x=-25\\\\x=25`

So, the value of x is 25.