Question

In rhombus ABCD, what is
∠
? Explain or show your work.

Answer 1

`\sf\\m\angle ADC=120^o`

Step-by-step explanation:

`\sf\\(i)\ AB=BC=CD=AD=9cm\ \ \ \textsf{[All sides of rhombus are equal.]}\\\\(ii)\ BE=ED=4.5cm,\ i.e.\ BD=9cm\ \ \ \textsf{[Diagonals of a rhombus bisect each}\\\textsf{\ \ \ \ \ each other.]}`

`\sf\\\textsf{(iii)\ }\triangle ABD\textsf{ is an equilateral triangle.}\ \ \ \textsf{[AB = BD = AD = 9cm]}`

`\sf\\(iv)\ \angle A=60^o\ \ \ \textsf{[Triangle ABD is equilateral, so all of it's angles are }60^o.]`

`\sf\\(v)\ \angle A+\angle ADC=180^o\ \ \ [\textsf{Sum of co-interior angles is }180^o.]\\\textsf{or, }60^o+\angle ADC=180^o\\\textsf{or, }\angle ADC=120^o`