Question

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

Answer 1

Answer:

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

$27$

The value of y is;

$y=9$

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;

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

Therefore, the value of y is;

$y=9$