Question

If the measures of the angles of a triangle are $\left(2x-5\right)°,{\left(3x-\frac{1}{2}\right)}^{°}\mathrm{and}{\left(30-\frac{x}{2}\right)}^{°}$, then x =
(a) $\frac{311}{9}$
(b) $\frac{309}{9}$
(c) $\frac{310}{9}$
(d) $\frac{301}{9}$

Answer 1

$$\begin{gathered} \left(2x-5\right)°+{\left(3x-\frac{1}{2}\right)}^{°}+{\left(30-\frac{x}{2}\right)}^{°}=180°\left[\mathrm{Angle}\mathrm{sum}\mathrm{property}\mathrm{of}\mathrm{triangle}\right] \\ \Rightarrow 2x-5+3x-\frac{1}{2}+30-\frac{x}{2}=180 \\ \Rightarrow 2x+3x-\frac{x}{2}-5-\frac{1}{2}+30=180 \\ \Rightarrow 4x+6x-x-10-1+60=180\times 2 \\ \Rightarrow 9x+49=360 \\ \Rightarrow 9x=311 \\ \Rightarrow x=\frac{311}{9} \end{gathered}$$
Hence, the correct answer is option (a).