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In \(\triangle ABC\), \(m\angle A =20^\circ\) and \(m\angle B = 35^\circ.\) Which of the following is true?

(A) \(\ \ AC = AB > BC\)

(B) \(\ \ AC > BC > AB\)

(C) \(\ \ AB > AC = BC\)

(D) \(\ \ AB > AC > BC\)

(E) \(\ \ BC > AC > AB\)

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In the figure above, points \(A, C,\) and \(D\) are collinear and \(\triangle ABC\) is isosceles, with \(AB=BC.\) If \(x=67,\) which of the following is true?

(A) \(\ \ y = 113\)

(B) \(\ \ AC > AB+BC\)

(C) \(\ \ y < z\)

(D) \(\ \ x + y = 159\)

(E) \(\ \ BD > BA\)

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The perimeter of \(\triangle ABC\) is \(\frac{1}{4}\) of the perimeter of \(\triangle DEF.\) If \(\triangle ABC\) is equilateral, and the perimeter of \(\triangle DEF\) equals \(156,\) what is the length of \(\overline{AB}?\)

(A) \(\ \ 4\)

(B) \(\ \ 13\)

(C) \(\ \ 39\)

(D) \(\ \ 52\)

(E) \(\ \ 156\)

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In the figure above, the \(AD:DB = 2:19.\) What is the ratio of the area of \(\triangle ADC\) to the area of \(\triangle ABC?\)

(A) \(\ \ 2:19\)

(B) \(\ \ 2:21\)

(C) \(\ \ 19:21\)

(D) \(\ \ 4:361\)

(E) \(\ \ 4:441\)

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\(\)

In the figure above, \(a=60\) and \(b=16.\) What is the value of \(x+y?\)

(A) \(\ \ 16\)

(B) \(\ \ 44\)

(C) \(\ \ 76\)

(D) \(\ \ 104\)

(E) \(\ \ 208\)

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