Question
Find the unknown marked angles 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} & \left(\mathrm{m}^{\circ}-5^{\circ}\right)+60^{\circ}+\left(\mathrm{m}^{\circ}+5^{\circ}\right)=180^{\circ} \\ & \Rightarrow \mathrm{m}^{\circ}-5^{\circ}+60^{\circ}+\mathrm{m}^{\circ}+5^{\circ}=180^{\circ} \\ & \Rightarrow 2 \mathrm{~m}^{\circ}=180^{\circ}-65^{\circ}+5^{\circ} \\ & \Rightarrow 2 \mathrm{~m}^{\circ}=120^{\circ} \\ & \Rightarrow \mathrm{m}^{\circ}=\frac{120^{\circ}}{2}=60^{\circ} \end{aligned} $
Hence $\angle A=m^{\circ}-5^{\circ}=60^{\circ}-5^{\circ}=55^{\circ}$
and $\angle \mathrm{C}=\mathrm{m}^{\circ}+5^{\circ}=60^{\circ}+5^{\circ}=65^{\circ}$
$ \begin{aligned} & \left(\mathrm{m}^{\circ}-5^{\circ}\right)+60^{\circ}+\left(\mathrm{m}^{\circ}+5^{\circ}\right)=180^{\circ} \\ & \Rightarrow \mathrm{m}^{\circ}-5^{\circ}+60^{\circ}+\mathrm{m}^{\circ}+5^{\circ}=180^{\circ} \\ & \Rightarrow 2 \mathrm{~m}^{\circ}=180^{\circ}-65^{\circ}+5^{\circ} \\ & \Rightarrow 2 \mathrm{~m}^{\circ}=120^{\circ} \\ & \Rightarrow \mathrm{m}^{\circ}=\frac{120^{\circ}}{2}=60^{\circ} \end{aligned} $
Hence $\angle A=m^{\circ}-5^{\circ}=60^{\circ}-5^{\circ}=55^{\circ}$
and $\angle \mathrm{C}=\mathrm{m}^{\circ}+5^{\circ}=60^{\circ}+5^{\circ}=65^{\circ}$
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