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:

76°

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 \({76}^\circ\).