Question

According to the diagram, how far is point L from Rays KH and HF?Find the value of Y

Answer 1

The distance between L and the line KH and HF is;

`27`

The value of y is;

`y=9`

Step-by-step explanation:

Given the figure in the attached image;

`\begin{gathered} KL=27 \\ KHL=(6y)^(\circ) \\ FHL=(4y+18)^(\circ) \end{gathered}`

From the image;

`KL=FL=27`

So, the distance between L and the line KH and HF is;

`27`

Also, the triangles KHL and FHL are congruent.

So, the angles KHL and FHL are congruent.

`m\measuredangle KHL\cong m\measuredangle FHL`

Substituting the expressions;

`\begin{gathered} (6y)^(\circ)=(4y+18)^(\circ) \\ 6y=4y+18 \\ 6y-4y=18 \\ 2y=18 \\ y=(18)/(2) \\ y=9 \end{gathered}`

Therefore, the value of y is;

`y=9`