Question

What is the value of x?



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Answer 1

`x=5`

Explanation:

We have been given a triangle. We are asked to find the value of x for our given triangle.

We can see that measures of both angles with red mark are equal.

The angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Using angle bisector theorem, we can set an equation as:

`(3x)/(15)=(2x-1)/(9)`

`15(2x-1)=3x(9)`

`30x-15=27x`

`30x-27x-15=27x-27x`

`3x-15=0`

`3x-15+15=0+15`

`3x=15`

`(3x)/(3)=(15)/(3)`

`x=5`

Therefore, the value of x is 5.