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Find the values of the variables so that the figure is aparallelogram.

Find the values of the variables so that the figure is aparallelogram.-example-1
User Atondelier
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Answer:

The image is given below as

From the image above, we can deduce that


\begin{gathered} \angle GEF=\angle DFE(altenate\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{hence,} \\ \angle DFE=64^0 \end{gathered}
\begin{gathered} \angle GEF=\angle BGH(correspond\in g\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{Hence,} \\ \angle BGH=64^0 \end{gathered}
\begin{gathered} \angle DFE+\angle HFE=180^0(\text{ linear pair sum up to give 180)} \\ \angle DFE=64^0 \\ \angle HFE=y \\ 64^0+y=180^0 \\ \text{collect similar terms, we will have} \\ y=180^0-64^0 \\ y=116^0 \end{gathered}

From the image also, we will have that


\begin{gathered} \angle BGH=\angle FHG(alternate\text{ angles)} \\ \angle BGH=64^0 \\ \angle FHG=x \\ \text{hence,} \\ x=64^0 \end{gathered}

Hence,

The value of x= 64°

The value of y = 116°

Find the values of the variables so that the figure is aparallelogram.-example-1
User Lele
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