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Geometry and Measurement

SAT Lines and Angles

\(\)

In the figure above, \(\overline{OB}\) bisects \(\angle AOC\) and \(\overline{OD}\) bisects \(\angle COE.\) If \(m \angle AOB = 50^\circ,\) what is the measure of \(\angle DOE?\)

(A) \(\ \ 25\)
(B) \(\ \ 40\)
(C) \(\ \ 80\)
(D) \(\ \ 100\)
(E) \(\ \ 130\)

\(A, B\) and \(C\) are points on a line. If \(AB=11\) and \(BC=2,\) which of the following statements could be true?

\(\begin{array}{l l l c l} &\text{I.} &AC &=& 9\\ &\text{II.} &AC &=& 11\\ &\text{III.} &AC &=& 13\\ \end{array}\)

(A) \(\ \ \)I only
(B) \(\ \ \)III only
(C) \(\ \ \)I and II only
(D) \(\ \ \)I and III only
(E) \(\ \ \)I, II, and III

\( \)

In the figure above, \(B\) is the midpoint of \(\overline{AE},\) \(C\) is the midpoint of \(\overline{AB},\) and \(D\) is the midpoint of \(\overline{CB}.\) If \(DB=9,\) what is the length of \(\overline{DE}?\)

(A) \(\ \ 9\)
(B) \(\ \ 18\)
(C) \(\ \ 27\)
(D) \(\ \ 36\)
(E) \(\ \ 45\)

\( \)

In the above diagram, \(\overline{AD}\), \(\overline{BE}\), and \(\overline{CF}\) are straight lines and \(m \angle AOB = a^\circ = 69^\circ, m \angle COD = b^\circ = 32^\circ,\) and \(m \angle FOE = x^\circ.\) Which of the following is the value of \(x\)?

(A) \(\ \ 32\)
(B) \(\ \ 79\)
(C) \(\ \ 101\)
(D) \(\ \ 143\)
(E) \(\ \ 281\)

\(\)
If the measure of \(\angle p\) is \(51^\circ\), what is the measure of \(\angle s?\)

(A) \(\ \ 39\)
(B) \(\ \ 51\)
(C) \(\ \ 90\)
(D) \(\ \ 129\)
(E) \(\ \ 141\)

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