question_answer

In a triangle ABC, \[\angle A=70{}^\circ ,\]\[\angle B=80{}^\circ \]and D is the in Centre of \[\Delta \,ABC.\] If \[\angle ACB=2x{}^\circ \]and \[\angle BDC=y{}^\circ .\]Then values of x and y, respectively are [SSC CGL Tier II, 2017]

A) 15,130

B) 15,125

C) 35, 40

D) 30,150

Correct Answer: B

Solution :

[b] In the adjoining figure, \[\angle ACB=30{}^\circ \]and \[\angle ACB=2x{}^\circ \](Given \[\Rightarrow \]\[30{}^\circ =2x{}^\circ \])                         \[\Rightarrow \]\[x=15{}^\circ \]and \[\angle BDC=y{}^\circ \]      (Given) From figure, \[\angle BDC=\left[ 180{}^\circ -\left( \frac{\angle ABC}{2}+\frac{\angle ACB}{2} \right) \right]\] \[y{}^\circ =\left[ 180{}^\circ -\left( \frac{80{}^\circ }{2}+\frac{30{}^\circ }{2} \right) \right]=[180{}^\circ -(40{}^\circ +15{}^\circ )]\] \[y=(180{}^\circ -55{}^\circ )\]\[\Rightarrow \]\[y=125{}^\circ \]\[\therefore \]x and y = 15 and 125