question_answer

\[\overrightarrow{\text{XY}}\] divides \[\angle \text{MXN=72}{}^\circ \] in the ratio 1:2. What is the measure of \[\angle \text{YXN}\]?

A) \[\text{48 }\!\!{}^\circ\!\!\text{ }\]                                          

B) \[\text{24 }\!\!{}^\circ\!\!\text{ }\]

C) \[\text{72 }\!\!{}^\circ\!\!\text{ }\]                        

D) \[\text{96 }\!\!{}^\circ\!\!\text{ }\]

Correct Answer: A

Solution :

Given \[\angle MXN=72{}^\circ \] and \[\overrightarrow{\text{XY}}\] divides \[\angle \text{MXN}\] in the ratio 1:2. \[\angle YXN=\frac{2}{3}\angle MXN=\frac{2}{3}\times 72{}^\circ =48{}^\circ \]