Question

The vertical angle of an isosceles triangle is 2/3 each of its base angles. Find it in radians.

Answer 1

Dear student
$$\begin{gathered} eachofthebaseanglehasmeasurex. \\ thenx+x+\frac{2}{3}x=180°[\mathrm{By}\mathrm{angle}\mathrm{sum}\mathrm{property}\mathrm{of}\mathrm{triangle}] \\ \Rightarrow \frac{3\mathrm{x}+3\mathrm{x}+2\mathrm{x}}{3}=180° \\ \Rightarrow 8\mathrm{x}=540° \\ \Rightarrow \mathrm{x}=67.5° \\ \Rightarrow \mathrm{x}={\left(67.5\times \frac{\mathrm{\pi }}{180}\right)}^{\mathrm{c}} \\ \Rightarrow \mathrm{x}=\frac{3\mathrm{\pi }}{8}\mathrm{radians} \end{gathered}$$
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