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

Answer:

x = 25

Step-by-step 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.