If the three angles of a triangle are: (x + 15 )^ , ( 6x5 + 6 )^ and ( 2x3 + 30 )^ then the triangle is:

Answer: Option B

According to question,
 $$\Rightarrow \left(x+{15}^{\circ }\right)+{\left(\frac{6x}{5}+6\right)}^{\circ }+$$      $${\left(\frac{2x}{3}+30\right)}^{\circ }=$$    $$180^{\circ }$$
 $$\left\{\angle A+\angle B+\angle C={180}^{\circ }\right\}$$
 $$\Rightarrow x+\frac{6x}{5}+\frac{2x}{3}=$$     $$180^{\circ }-\left(15+6+30\right)$$
$$\begin{array}{rl}& \Rightarrow \frac{15x+18x+10x}{15}=180-51\\ & \Rightarrow 43x=129\times 15\\ & \Rightarrow x=45^{\circ }\\ & \Rightarrow \text{each}\text{angle}\\ & \Rightarrow {\left(x+15\right)}^{\circ }=45+15=60^{\circ }\\ & \Rightarrow {\left(\frac{6x}{5}+6\right)}^{\circ }=60^{\circ }\\ & \Rightarrow {\left(\frac{2x}{3}+30\right)}^{\circ }=60^{\circ }\end{array}$$
∵ All three angles are equal 60°
⇒ Triangle will be equilateral triangle