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

Don Leatham asked Jun 21, 2022

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25 votes

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

Don Leatham asked Jun 21, 2022

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16 votes

Answer:

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
$\Longleftarrow$

OAmalOHopeO

Colla answered Jun 25, 2022

by Colla

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