Answer: m∠[tex]E=74\°[/tex]
Step-by-step explanation:
1. By definition, the adjacent angles of a parallelogram are supplementary, they add up 180 degrees. Therefore, in the given parallelogram:
[tex]O+M=180[/tex]
[tex]3x+1+2x+4=180[/tex]
2. Then, you must solve for x, as following:
[tex]5x+5=180[/tex]
[tex]5x=175\\x=35[/tex]
3. Substitute the value of x obtained into [tex]2x+4[/tex] to calculate the angle M:
[tex]2x+4=2(35)+4=74[/tex]
Then:
m∠[tex]M=74\°[/tex]
4. By definition the opposite angles of a parallelogram are equal, therefore:
[tex]E=M\\E=74\°[/tex]
