Question

What is the value of x?



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Answer 1

Answer:

$x=5$

Step-by-step 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:

$\frac{3x}{15}=\frac{2x-1}{9}$

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

$30x-15=27x$

$30x-27x-15=27x-27x$

$3x-15=0$

$3x-15+15=0+15$

$3x=15$

$\frac{3x}{3}=\frac{15}{3}$

$x=5$

Therefore, the value of x is 5.