Question
Find the value of the angle in the given figure:
✓
Answer
In the figure,
$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ} $......... (Sum of angles of a triangle)
$ \begin{aligned} & \Rightarrow 5 x^{\circ}+4 x^{\circ}+x^{\circ}=180^{\circ} \\ & \Rightarrow 10 x^{\circ}=180^{\circ} \end{aligned} $
$ \Rightarrow \mathrm{x}=\frac{180^{\circ}}{10}=18^{\circ} $
$ \therefore \angle \mathrm{A}=5 \mathrm{x}^{\circ}=5 \times 18^{\circ}=90^{\circ} $
$ \angle B=4 x=4 \times 18^{\circ}=72^{\circ} $
and $\angle C=x=18^{\circ}$
$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ} $......... (Sum of angles of a triangle)
$ \begin{aligned} & \Rightarrow 5 x^{\circ}+4 x^{\circ}+x^{\circ}=180^{\circ} \\ & \Rightarrow 10 x^{\circ}=180^{\circ} \end{aligned} $
$ \Rightarrow \mathrm{x}=\frac{180^{\circ}}{10}=18^{\circ} $
$ \therefore \angle \mathrm{A}=5 \mathrm{x}^{\circ}=5 \times 18^{\circ}=90^{\circ} $
$ \angle B=4 x=4 \times 18^{\circ}=72^{\circ} $
and $\angle C=x=18^{\circ}$
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