Question 1013107


given:

E || F
AB is perpendicular to F, => AB is perpendicular to E because E || F
AG is the perpendicular bisector of CD-> I think it should be BG is the perpendicular bisector of CD


If {{{m}}} < {{{C-AB-D = 30}}} (this is angle between line segment AB and plane in which triangle ACD lie),  is same as {{{m}}} <G-A-B=30}}} (angle between line segments {{{GA}}} and {{{AB}}})

since {{{BG}}} is the perpendicular bisector of {{{CD}}}, means line segment {{{CG=GD}}}, consequently {{{BC=BD}}}; so, triangle {{{BCD}}} is divided into two right triangles by {{{ BG }}}
then we know that:
1. measure of angles vertex {{{B}}}  and {{{G}}} is {{{90 }}}
2. sides {{{BC}}} and {{{BD}}} are equal in length, then triangles {{{ABG}}}, {{{BCG}}}, and {{{BGD}}} are right triangles which are {{{similar}}}

take a look at similar triangles {{{ABG}}}  and {{{BGD}}}:

angles vertex  {{{B}}} and {{{G}}}  are both {{{90 }}}
{{{AG}}} corresponds to {{{BD}}}
{{{GD }}}correspond to {{{AB}}}
{{{ BG }}}is common side 

if {{{AG}}} corresponds to {{{BD}}} and {{{m}}} < {{{ABG =30}}} , then  the {{{m}}} < {{{GBD =30}}} too

consequently

 {{{m}}} < {{{BDC =60}}}