Question
Find the unknown angles in the given figure:
✓
Answer
In the figure,
$ x=y $ ........ (Angles opposite to equal sides)
But $x+y+90^{\circ}=180^{\circ}$ ....... (Angles of a triangle)
$ \Rightarrow x+x+90^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}+90^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}=180^{\circ}-90^{\circ}=90^{\circ} $
$ \therefore \mathrm{x}=\frac{90^{\circ}}{2}=45^{\circ} $
$ \therefore \mathrm{y}=\mathrm{x}=45^{\circ} $
Hence $x=45^{\circ}, y=45^{\circ}$
$ x=y $ ........ (Angles opposite to equal sides)
But $x+y+90^{\circ}=180^{\circ}$ ....... (Angles of a triangle)
$ \Rightarrow x+x+90^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}+90^{\circ}=180^{\circ} $
$ \Rightarrow 2 \mathrm{x}=180^{\circ}-90^{\circ}=90^{\circ} $
$ \therefore \mathrm{x}=\frac{90^{\circ}}{2}=45^{\circ} $
$ \therefore \mathrm{y}=\mathrm{x}=45^{\circ} $
Hence $x=45^{\circ}, y=45^{\circ}$
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