Question

given that (overrightarrow{eb}) bisects (angle cea), which statements must be true? select three options. (square mangle cea = 90^{circ}) (square mangle cef=mangle cea + mangle bef) (square mangle ceb = 2(mangle cea)) (squareangle cef) is a straight angle. (squareangle aef) is a right angle.

Explanation:

Step1: Analyze each option

• For \(m\angle CEA = 90^{\circ}\): There is no information in the problem stating that \(\angle CEA\) is a right - angle.
• For \(m\angle CEF=m\angle CEA + m\angle BEF\): Since \(\overrightarrow{EB}\) bisects \(\angle CEA\), this formula is incorrect.
• For \(m\angle CEB = 2(m\angle CEA)\): Since \(\overrightarrow{EB}\) bisects \(\angle CEA\), it should be \(m\angle CEA=2m\angle CEB\).
• For \(\angle CEF\) is a straight angle: A straight angle measures \(180^{\circ}\). Points \(C\), \(E\), and \(F\) are collinear, so \(\angle CEF = 180^{\circ}\) (by the definition of a straight - angle).
• For \(\angle AEF\) is a right angle: \(\angle AEC+\angle AEF = 180^{\circ}\) (linear pair). If \(\angle AEC = 90^{\circ}\) (assume from the perpendicular symbol in the figure, though not explicitly stated in the text but from the visual), then \(\angle AEF=90^{\circ}\) (right - angle).

Answer:

\(\angle CEF\) is a straight angle, \(\angle AEF\) is a right angle.