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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.​

Respuesta :

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.

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