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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles3 Marks
Question
In the given figure, $AB\ ||\ CD$ and $EF$ is a transversal. If $\angle\text{AEF}=65^\circ,\angle\text{DFG}=30^\circ,\angle\text{EFG}=90^\circ$ and $\angle\text{GEF}=\text{x}^\circ,$ find the value of $x$.
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Answer

$AB\ ||\ CD$ and $EF$ is the transversal.
$\Rightarrow\angle\text{AEF}=\angle\text{EFD}$ (alternate angles)
$\Rightarrow\angle\text{AEF}=\angle\text{EFG}+\angle\text{DFG}$
$\Rightarrow65^\circ=\angle\text{EFG}+30^\circ$
$\Rightarrow\angle\text{EFG}=35^\circ$ In $\triangle\text{GEF},$ by angle sum property,
$\angle\text{GEF}+\angle\text{EGF}+\angle\text{EFG}=180^\circ$
$\Rightarrow\text{x}+90^\circ+35^\circ=180^\circ$
$\Rightarrow\text{x}=55^\circ$

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