in a rhombus ABCD, angle ABC = 64 degrees. calculate angle BCD, angle ADB and angle BAC.

Question

GEOMETRY of o levels

 

Answer 1

the information that is most helpful is

 

1. opposite angles are congruent because a rhombus is a parallelogram, not necessarily because all sides are equal.

2. adjacent angles are supplementary

3. the diagonals of a rhombus bisect the angles because the sides are all congruent as they are in a square.

 

Therefore angle BCD=180-64=116 degrees, angle ADB=(1/2)64=32 degrees, and angle BAC=(1/2)116=58 degrees.

Answer 2

The fours sides of a rhombus are of equal length. This also means that opposite angles of a rhombus have equal measure. The interior angles add up to 360 because there are four side. (n-2)(180)=Interior Angle; where n=number of sides. So if the opposite angles are equal then if ABC=64, ABD=ABC=64. You can solve for the other angles as they will be complementary. So BCD=90-64=26 and because the other two angles are opposites BCD=BAC=26.