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Lines and Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Triangles3 Marks
Question
In the given figure, AB || CD. Find the value of x.

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Answer

Since AB || CD and BC is a transversal.
So, $\angle\text{BCD}=\angle\text{ABC}=\text{x}^\circ$ [Alternate angles]
As BC || ED and CD is a transversal.
$\angle\text{BCD}+\angle\text{EDC}=180^\circ$
$\Rightarrow\angle\text{BCD}+75^\circ=180^\circ$
$\Rightarrow\angle\text{BCD}=180^\circ-75^\circ=105^\circ$
$\Rightarrow\angle\text{ABC}=105^\circ$ $[$ Since $\angle\text{BCD}=\angle\text{ABC}]$
$\therefore\text{x}^\circ=\angle\text{ABC}=105^\circ$
Hence, $\text{x}=105.$

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