Question

one of the diagonals of a rhombus is equal to its sides. find the measure of all the angles of the Rhombus​

Answer 1

Answer:

<A = 120 degree

< B = 60 degree

<C = 120 degree

<D = 60 degree

Step-by-step explanation:

(Draw the below explanation for better understanding)

Consider rhombus ABCD and diagonal BD

Triangle ABD is an equilateral triangle.(sides of a rhombus are equal and diagonal is equal to its sides)

Therefore, angle B= 60 degree(each angle = 60 degree in an equilateral triangle)

< B =<D = 60 degree (opposite angles are equal)

<A+<B = 180 degree (adjacent sides)

<A = 180-<B = 180-60 = 120 degree

<A=<C = 120 degree(opposite angles are equal)

Therefore, <A = 120 degree

                  < B = 60 degree

                  <C = 120 degree

                  =<D = 60 degree