Question

8. One diagonal of a rhombus is equal to its side. Find all the angles of the rhombus.

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Answer 1

Let ABCD be a rhombus

AB = BC ........... ( 1) ( given )

BC =AB ............(2) ( side of rhombus )

From equations (1) and ( 2) ,

AC= BC= AB

this implies ABC is equilateral triangles

so, angle BAC = angle CAB = 60⁰ ...... (3)

similarly triangle DAC is also an equilateral triangle

angle CAD = DCA = ADC = 60⁰ ....... ( 4)

from equations (3 ) and ( 4 ) , we get

angle ( BCA + DCA ) =60⁰ + 60⁰

=120⁰

angle C = angle A = 120⁰

angle B = angle D =60⁰