Question

given: (overrightarrow{eb}) bisects (angle aec). (angle aed) is a straight angle. prove: (mangle aeb = 45^{circ}) complete the paragraph proof. we are given that (overrightarrow{eb}) bisects (angle aec). from the diagram, (angle ced) is a right angle, which measures (square) degrees. since the measure of a straight angle is (180^{circ}), the measure of angle (square) must also be (90^{circ}) by the (square). a bisector cuts the angle measure in half. (mangle aeb) is (45^{circ}).

Explanation:

• A right angle measures \(90^{\circ}\), so \(\angle CED = 90^{\circ}\).
• Since \(\angle AED\) is a straight angle (\(180^{\circ}\)), and \(\angle AEC+\angle CED=\angle AED\) (angle - addition postulate), if \(\angle CED = 90^{\circ}\), then \(\angle AEC=180^{\circ}-\angle CED = 90^{\circ}\).

Answer:

• The first blank: \(90\)
• The second blank: \(\angle AEC\)
• The third blank: angle - addition postulate