contestada

In the diagram below of triangle DEF, G is a midpoint of D E and H is a midpointof EF. If MZGHE = x + 52, and mZDFH = 96 – 102, what is the measureof ZDFH?

Respuesta :

According to the given figure, angles GHE and DFH are corresponding angles, which are equal because GH and DF are parallels. So, we can express the following

[tex]m\angle GHE=m\angle DFH[/tex]

Replacing the given expressions, we have

[tex]x+52=96-10x[/tex]

Let's solve for x

[tex]\begin{gathered} x+10x=96-52 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]

Then, we find the measure of the angle DFH

[tex]\begin{gathered} m\angle DFH=96-10x=96-10\cdot4=96-40 \\ m\angle DFH=56 \end{gathered}[/tex]

Hence, the angle DFH measures 56°.