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Hint :
Equilateral triangle has same sides and same angles.
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Suppose that one of the angles has a measure of y .
So angles are : y , y and y
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Sum of the interior angles of any triangle is 180° .
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According above :
[tex]y + y + y = 180°[/tex]
[tex]3y = 180°[/tex]
Divide sides by 3
[tex] \frac{3y}{3} = \frac{180}{3} \\ [/tex]
[tex]y = 60°[/tex]
We found that the measure of the angles are equal , so this is the measure of all three angles.
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Question gave us one of the angles as
4x -12 .
So ;
[tex]4x - 12 = 60[/tex]
Add sides 12
[tex]4x - 12 + 12 = 60 + 12[/tex]
[tex]4x = 72[/tex]
Divide sides by 4
[tex] \frac{4x}{4} = \frac{72}{4} \\ [/tex]
[tex]x = \frac{9 \times 2 \times 4}{4} \\ [/tex]
[tex]x = 9 \times 2[/tex]
[tex]x = 18[/tex]
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We found that sides are same ,
So :
[tex]BZ = DB = DZ = 7x + 119 \\ [/tex]
Thus :
[tex]DB = 7x + 119[/tex]
[tex]DB = 7(18) + 119[/tex]
[tex]DB = 126 + 119[/tex]
[tex]DB = 245[/tex]
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The correct answer is Option three .
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