SOLUTION: ABCD is a rhombus whose diagonals AC and BD intersect at M. If ∠DAB=110o, find ∠BDC.
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Question 828016: ABCD is a rhombus whose diagonals AC and BD intersect at M. If ∠DAB=110o, find ∠BDC.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
A rhombus is just a parallelogram which has 4 equal sides. So anything that is true about a parallelogram is also true for a rhombus. In particular, the opposite sides in a parallelogram (and therefore in a rhombus) are parallel.
This makes consecutive angles in a parallelogram (or rhombus) same-side (or consecutive) interior angles. When two parallel lines are intersected by a transversal, the same-side interior angles are always supplementary.
Angle DAB and angle BDC are consecutive angles in this rhombus. So they must be supplementary. So they must add up to 180. So angle BDC must be 70 (since 110 + 70 = 180).
Draw a diagram if you're having trouble understanding this.
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