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Geometry and Measurement

SAT Parallel Lines

\(\)

In the figure above, \(m \parallel n.\) If \(\overline{CB}\) bisects \(\angle ACD,\) and \(a = 28^\circ,\) what is the value of \(b?\)

(A) \(\ \ 14\)
(B) \(\ \ 28\)
(C) \(\ \ 76\)
(D) \(\ \ 90\)
(E) \(\ \ 104\)

\(\)

If \(m \parallel n\) and \(w = 40,\) what is the value of \(x + y + z?\)

(A) \(\ \ 40\)
(B) \(\ \ 80\)
(C) \(\ \ 180\)
(D) \(\ \ 220\)
(E) \(\ \ 260\)

\( \)

In the figure above, line \(p\) is perpendicular to line \(m.\) If \(a < 90,\) which of the following could be true?

(A) \(\ \ b = 80\)
(B) \(\ \ b = 90\)
(C) \(\ \ b = 100\)
(D) \(\ \ a = b\)
(E) \(\ \ n \parallel m\)

\(\)

In the figure above, \(a \parallel b\) and \(c \parallel d.\) If \(w = 100^\circ,\) what is the sum of \(x, y,\) and \(z?\)

(A) \(\ \ 20\)
(B) \(\ \ 180\)
(C) \(\ \ 200\)
(D) \(\ \ 280\)
(E) \(\ \ 220\)

\(\)

In the figure above, \(m \parallel n\). If \(a = 115\) and \(b = 140,\) which of the following equals \(y-x?\)

(A) \(\ \ 0\)
(B) \(\ \ 25\)
(C) \(\ \ 115\)
(D) \(\ \ 140\)
(E) \(\ \ 255\)

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