A) \[\text{10 }\!\!{}^\circ\!\!\text{ }\]
B) \[\text{20 }\!\!{}^\circ\!\!\text{ }\]
C) \[\text{30 }\!\!{}^\circ\!\!\text{ }\]
D) \[\text{40 }\!\!{}^\circ\!\!\text{ }\]
Correct Answer: D
Solution :
Let the angles of the triangle be \[2x,\text{ }3x\] and\[4x\]. As sum of angles of a triangle Is\[\text{180 }\!\!{}^\circ\!\!\text{ }\] \[\therefore \] \[2x+3x+4x=180{}^\circ \] \[\Rightarrow 9x=180{}^\circ \Rightarrow x=\frac{180{}^\circ }{9}=20{}^\circ \] So, the angles are \[2x=2\times 20{}^\circ =40{}^\circ \] \[3x=3\times 20{}^\circ =60{}^\circ \] \[4x=4\times 20{}^\circ =80{}^\circ \] \[\therefore \] Difference between the greatest and smallest angles \[=\text{ }80{}^\circ -40{}^\circ =40{}^\circ \]
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