Question

Diagonal ac of a rhombus abcd is equal to side bc find all angles of this rhombus

Answer 1

In triangle ABC

BC=AB.. all sides of a rhombus are congruent.

AC=BC.. given

therefore AB=BC=AC ∆ ABC is a equilateral triangle

all angles of a equilateral triangle =60°

therefore Angle ABC of Rhombus is 60°...proved

Similarly we can prove that angle ADC =60°

adjacent angles of a rhombus are supplementary

therefore

angle DAB+ + angle ABC equal to 180 degree.

angle DAB = 180 - 60

angle DAB equal to 120 degree

angle DCB equal to 120 degree ...opposite angles of rhombus are equal