In ΔABC, BD ⊥ AC at D. E is a point on BC such that ∠BEA = x°. If ∠EAC = 46° and ∠EBD = 60°, then the Ans value of x is:
Answer & explanation
Correct answer: option 4
Given BD is perpendicular to AC at D
\(\angle\)BDC = \({90}^\circ\)
In \(\Delta \)BDC,
\(\angle\)EBD = \({60}^\circ\) and \(\angle\)BDC = \({90}^\circ\)
\(\angle\)DCB = \({180}^\circ\) - \({(60\; + \; 90)}^\circ\)
\(\angle\)DCB = \({30}^\circ\)
In \(\Delta \)AEC,
\(\angle\)EAC = \({46}^\circ\) and \(\angle\)ACE = \({30}^\circ\)
\(\angle\)AEC = \({180}^\circ\) - \({(46\; + \; 30)}^\circ\)
\(\angle\)DCB = \({104}^\circ\)
\(\angle\)BEA = \({180}^\circ\) - \(\angle\)AEC
= \(\angle\)BEA = \({180}^\circ\) - \({104}^\circ\)
= \(\angle\)BEA = \({76}^\circ\)
Therefore, the value of x is \({76}^\circ\).