Question
The angle bisector of ∠ACD in rhombus ABCD makes a 64° angle with the diagonal
BD
. Find the measure of ∠BAD.
BD
. Find the measure of ∠BAD.
Answers
Steve
Huh?
The angle bisector is the diagonal AC.
The diagonals of a rhombus are perpendicular.
The angle bisector is the diagonal AC.
The diagonals of a rhombus are perpendicular.
Reiny
Assuming you made a sketch.
Let the angle bisector of ∠ACD meet BD at E
let the diagonals intersect at F
In a rhombus the diagonals right-bisect each other.
So, in triangle CEF, angle F = 90
angle E = 64, thus angle FCE = 26°
which makes angle BCD = 104°
and of course ∠BAD = 104°
Let the angle bisector of ∠ACD meet BD at E
let the diagonals intersect at F
In a rhombus the diagonals right-bisect each other.
So, in triangle CEF, angle F = 90
angle E = 64, thus angle FCE = 26°
which makes angle BCD = 104°
and of course ∠BAD = 104°
Steve
nice save, Reiny. I later realized how I had misread the problem.