In the given figure AB = DB and AC = DC. If $\angle A B D=58^{\circ}$ and $\angle DBC=(2x-4)^{\circ}, \angle A C B=(y+15)^{\circ}$ and $\angle D C B=63^{\circ}$, then the value of 2x + 5y is :
Answer & explanation
Correct answer: option 4
As AB = DB, AC = DC, and BC is common for two triangle
So, \(\Delta \)ABC = \(\Delta \)DBC
So, \(\angle\)ABC = \(\angle\)DBC = \(\angle\)ABD/2
⇒ \(\frac{58}{2}\) = \({29}^\circ\)
So,
\({2x\; -\; 4 }^\circ\) = \({29}^\circ\)
⇒ 2x = \({33}^\circ\)
Again,
\(\angle\)ACB = \(\angle\)DCB = \({63}^\circ\)
So,
(y + \({15}^\circ\)) = \({63}^\circ\)
⇒ y = \({48}^\circ\)
So,
2x + 5y = \({33}^\circ\) + 5 x \({48}^\circ\)
⇒ \({33}^\circ\) + \({240}^\circ\)
⇒ \({273}^\circ\)
Therefore, the answer is \({273}^\circ\)