Question

which statement is true about the given information? ∠ced measures 45°, ∠ced measures 180°, ∠aec measures 90°, ∠aec measures 45°.

Explanation:

Step1: Analyze the diagram

From the diagram, we can see that \( \angle CED \) is formed by a right angle (since there is a right - angle symbol between \( EC \) and \( ED \))? Wait, no. Wait, \( AE \) and \( ED \) are a straight line, and \( EC \) is perpendicular to \( ED \) (the right - angle symbol at \( E \) between \( EC \) and \( ED \)). So \( \angle CED = 90^{\circ}\)? Wait, no, let's re - examine. The right - angle symbol is between \( EC \) and \( AE \)? Wait, no, the diagram shows that at point \( E \), \( EC \) is perpendicular to \( AD \) (since \( AD \) is a straight line and there is a right - angle symbol between \( EC \) and \( AD \)). So \( \angle AEC=90^{\circ}\), because the right - angle symbol indicates a \( 90^{\circ}\) angle.

Let's check each option:

• Option 1: \( \angle CED \) measures \( 45^{\circ}\). Since \( EC \) is perpendicular to \( AD \), \( \angle CED = 90^{\circ}\), so this is false.
• Option 2: \( \angle CED \) measures \( 180^{\circ}\). A straight angle is \( 180^{\circ}\), but \( \angle CED \) is a right angle (from the diagram's right - angle symbol), so this is false.
• Option 3: \( \angle AEC \) measures \( 90^{\circ}\). The right - angle symbol at \( E \) between \( EC \) and \( AD \) (where \( AE \) is part of \( AD \)) indicates that \( \angle AEC = 90^{\circ}\), so this is true.
• Option 4: \( \angle AEC \) measures \( 45^{\circ}\). Since there is a right - angle symbol, it should be \( 90^{\circ}\), so this is false.

Answer:

\( \angle AEC \) measures \( 90^{\circ}\) (the option: \( \boldsymbol{\angle AEC \text{ measures } 90^{\circ}} \))