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.
