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makvit [3.9K]
3 years ago
8

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.​

Mathematics
1 answer:
Sonja [21]3 years ago
8 0

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.

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