Question

Given that ABCD is a rhombus, what is the value of x?

B
C.
(3x + 12)
D
A. 19.5
B. 78
C. 15.8
D. 26
E. 52
F. Cannot be determined

Answer 1

Diagonals of a rhombus intersect at right angles

Therefore,
`\angle AOD=90`

`Now,in\: \bigtriangleup AOD`

`\angle OAD+\angle AOD+\angle ADO=180`

`x+90+3x+12=180`
`\leftarrow [combing \: like\: terms]`

`4x+102=180\\-102 \: -102`
`\leftarrow [subtracting \:102 ]`

`(4x)/(4) =(78)/(4) \leftarrow [dividing \: by\: 4]`

`x=19.5`
`\Longleftarrow`

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