Question
Find the unknown angles in the given figure:
✓
Answer
In the figure,
$x=y$ ..(Angles opposite to equal sides)
But $x+y+80^{\circ}=180^{\circ}$ (Angles of a triangle)
$ \Rightarrow \mathrm{x}+\mathrm{x}+80^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}+80^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}=180^{\circ}-80^{\circ}=100^{\circ} $
$ \Rightarrow \mathrm{x}=\frac{100^{\circ}}{2}=50^{\circ} $
$ \therefore y=x=50^{\circ} $
Hence $x=50^{\circ}, y=50^{\circ}$
$x=y$ ..(Angles opposite to equal sides)
But $x+y+80^{\circ}=180^{\circ}$ (Angles of a triangle)
$ \Rightarrow \mathrm{x}+\mathrm{x}+80^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}+80^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}=180^{\circ}-80^{\circ}=100^{\circ} $
$ \Rightarrow \mathrm{x}=\frac{100^{\circ}}{2}=50^{\circ} $
$ \therefore y=x=50^{\circ} $
Hence $x=50^{\circ}, y=50^{\circ}$
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