Question

In the diagram below of triangle FGH, J is a midpoint of FG and K is a midpoint of GH. If mZJKG = 76 - 2x, and mZFHK = 6x – 4, what is the measure of ZJKG? G J K F H

Answer 1

In this problem the triangle FHG is similar to JKG because all the angles are equal so in this case we know that bout angles are equal so the expression will be:

`76-2x=6x-4`

so we solve for x so:

`\begin{gathered} 76+4=6x+2x \\ 80=8x \\ (80)/(8)=x \\ 10=x \end{gathered}`

So with the value of x we can find the angle JKG

`\begin{gathered} \angle JKG=76-2(10) \\ \angle JKG=76-20 \\ \angle JKG=56º \end{gathered}`