Question

Can you help me find the value of x?

Answer 1

x = 12

Explanation:

An angle bisector is a line, ray, or segment that divides an angle into two congruent angles.

The Angle Bisector Theorem states that in a triangle, when an angle bisector intersects the opposite side, it divides it into two segments whose lengths have a proportional relationship with the lengths of the other two sides of the triangle.

`\boxed{\sf (Segment\;1)/(Segment\;2)=(Side \;1)/(Side\;2)}`

From inspection of the given triangle, we can see that the angle between the sides labelled "15" and "20" has been bisected (divided into two equal parts). Therefore, according to the Angle Bisector Theorem:

`(x)/(9)=(20)/(15)`

Solve the equation for x by dividing both sides by 9:

`(x)/(9)\cdot 9=(20)/(15)\cdot 9`

`x=(180)/(15)`

`x = 12`

Therefore, the value of x is 12.

Answer 2

x = 12

Explanation:

the segment splitting the angle into 2 equal parts is an angle bisector

It divides the side opposite the angle into segments that are proportional to the other 2 sides , that is

`(x)/(9)` =
`(20)/(15)` ( cross- multiply )

15x = 9 × 20 = 180 ( divide both sides by 15 )

x = 12