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In the diagram below, rectangle ABCD has point E located on side CD such that AE=BE. If m

In The Diagram Below Rectangle ABCD Has Point E Located On Side CD Such That AEBE If M class=

Sagot :

Question Number 6

Answer: (4)

Explanation:

Angle D and C are 90 degrees, since ABCD is a rectangle.

From bottom left triangle, we can say:

[tex]\angle D+\angle\text{DAE}+\angle\text{AED}=180[/tex]

Putting the known information, we can solve for Angle AED:

[tex]\begin{gathered} \angle D+\angle\text{DAE}+\angle\text{AED}=180 \\ 90+61+\angle\text{AED}=180 \\ 151+\angle\text{AED}=180 \\ \angle\text{AED}=180-151 \\ \angle\text{AED}=29 \end{gathered}[/tex]

Also, Angle BEC = Angle AED

Thus,

Angle BEC = 29

Now, we know [ since straight line is 180 degrees]:

[tex]\angle\text{AED}+\angle\text{AEB}+\angle\text{BEC}=180[/tex][tex]\begin{gathered} \angle\text{AED}+\angle\text{AEB}+\angle\text{BEC}=180 \\ 29+\angle\text{AEB}+29=180 \\ \angle\text{AEB}=180-29-29 \\ \angle\text{AEB}=122\degree \end{gathered}[/tex]

The answer is (4), 122 degrees.

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