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Quadrilateral DEFG is a rhombus and m value of p
asked
Apr 28, 2023
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Quadrilateral DEFG is a rhombus and m value of p
Mathematics
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Nathanial
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1
Answer
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Solution:
Note that:
Opposite angles
are always
equal.
The sum of the degrees in a
quadrilateral
is
360°
This means that:
∠F = ∠D = 62°
∠E = ∠G = 5p + 49
∠F + ∠D + ∠E + ∠G = 360
Solving for p.
∠F + ∠D + ∠E + ∠G = 360
=> 62 + 62 + 5p + 49 + 5p + 49 = 360
=> p(5 + 5) + (62 + 62 + 49 + 49) = 360
=> p(10) + (222) = 360
=> 10p + 222 = 360
=> 10p = 360 - 222
=> 10p = 138
=> 10p/10 = 138/10
=>
p = 13.8
Check:
∠E = ∠G = 5p + 49
=> ∠E = ∠G = 5(13.8) + 49
=> ∠E = ∠G = 69 + 49
=>
∠E = ∠G = 118°
=> ∠F + ∠D + ∠E + ∠G = 360
=> 62 + 62 + 118 + 118 = 360
=>
360 = 360 (True)
Harshay Buradkar
answered
May 2, 2023
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Harshay Buradkar
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