Question

If one of the diagonal of a rhombus is equal to its sides find all angles of the
rhombus.​

Answer 1

Answer:

180°

Step-by-step explanation:

If we have the rhombus as one side is equal to the diagonal then we have the rhombus divided into two equilateral triangles. So, other angles are equal as that is a rhombus and two adjacent angles will give us sum as 180∘ .

Hey guys it will help you.

Answer 2

ABCD is A rhombus which means

AC= BC .....i

BC= AB......ii

from equation i and ii

AC=BC=AB

Triangle ABC is an euilateral triangle

so angle ABC = 60°

angle BCA = 60° ......iii

angle CAB= 60° ......iv

Similarly in triangle ADC

AD = DC ( sides of a rhombus)

AD = BC

but BC = AC

AD = AC

AD = DC = AC

Triangle DAC is an euilateral triangle

angle A = 60° ......v

angle D = 60°

angle C = 60° .......vi

from equation iii and vi we get

angle BCA + angle DCA = 60 + 60 = 120°

angle A = 120 °

Hence the angles of a rhombus are

120° , 60° , 120° , 60°