Question

which statement is true about the given information? ∠ced measures 45°. ∠aec measures 90°. ∠aec measures 45°. ∠ced measures 180°. (with a diagram of lines and angles at point e)

Explanation:

Step1: Analyze the diagram

From the diagram, we see that \( \angle CED \) has a right - angle symbol, so \( \angle CED = 90^{\circ}\). Also, \( \angle AEC\): since \( \angle AED\) is a straight angle (\(180^{\circ}\)) and \( \angle CED = 90^{\circ}\), and if we assume that \(EB\) bisects the angle between \(EA\) and \(EC\) (or by the right - angle and the structure), we can check the angle measures.

Step2: Evaluate each option

• Option 1: \( \angle CED\) measures \(45^{\circ}\): From the right - angle symbol, \( \angle CED = 90^{\circ}\), so this is false.
• Option 2: \( \angle AEC\) measures \(90^{\circ}\): Since \( \angle AED\) is a straight line (\(180^{\circ}\)) and \( \angle CED = 90^{\circ}\) (right angle), \( \angle AEC=180^{\circ}-\angle CED = 90^{\circ}\), so this is true.
• Option 3: \( \angle AEC\) measures \(45^{\circ}\): As we calculated above, \( \angle AEC = 90^{\circ}\), so this is false.
• Option 4: \( \angle CED\) measures \(180^{\circ}\): A straight angle is \(180^{\circ}\), but \( \angle CED\) is a right angle, so this is false.

Answer:

\( \angle AEC\) measures \(90^{\circ}\)