Thank you for visiting ABCD is a rectangle find m. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
The correct answer is [tex]\boxed{90^\circ}[/tex].
To find the measure of angle AEB in rectangle ABCD, we can use the properties of a rectangle. A rectangle is a type of parallelogram where all angles are right angles, meaning they measure [tex]\(90^\circ\)[/tex]. Since AE is a diagonal of rectangle ABCD, it connects two opposite vertices, A and B. When a diagonal of a rectangle is drawn, it bisects the rectangle into two congruent right triangles.
Angle AEB is formed at the intersection of the diagonal AE and the side BD of the rectangle. Because ABCD is a rectangle, angle ABD (which is the same as angle ABE because they are alternate interior angles formed by the transversal AE with lines AB and BD) is a right angle, measuring [tex]\(90^\circ\)[/tex]. Since angle AEB is a part of angle ABD, and angle ABD is [tex]\(90^\circ\)[/tex], it follows that [tex]m\(\angle\)AEB is also \(90^\circ\)[/tex].
Therefore, the measure of angle AEB is [tex]\(90^\circ\)[/tex], which is consistent with the properties of a rectangle.
Thank you for reading the article ABCD is a rectangle find m. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
Rewritten by : Jeany
Answer:
[tex]\Rightarrow m\angle AEB=130^{\circ}[/tex]
Step-by-step explanation:
As ABCD is a rectangle. So each angle of the rectangle is 90° and [tex]m\angle EAD=65^{\circ}[/tex], so
[tex]m\angle EAB=90^{\circ}-65^{\circ}=25^{\circ}[/tex]
The diagonals of the rectangle bisects each other. Hence,
[tex]\Rightarrow AE=BE[/tex]
In a triangle if two sides are equal then the angles opposite them will be equal.
So in triangle AEB,
[tex]m\angle EBA=m\angle EAB=25^{\circ}[/tex]
As the sum of the angles in a triangle adds up to 180°, so
[tex]\Rightarrow m\angle EBA+m\angle EAB+m\angle AEB=180^{\circ}[/tex]
[tex]\Rightarrow m\angle AEB=180^{\circ}- m\angle EBA-m\angle EAB[/tex]
[tex]\Rightarrow m\angle AEB=180^{\circ}-25^{\circ}-25^{\circ}=130^{\circ}[/tex]
