Answer:
1) Third option.
2) First option.
Step-by-step explanation:
1) By definition the opposite angles of a parallelogram are equal, then:
[tex]\angle Y=\angle W\\\\10x-27=2x+29[/tex]
Solving for "x", we get:
[tex]10x-2x=29+27\\\\8x=56\\\\x=7[/tex]
Then we can find the measure of the angle "W":
[tex]\angle W=2(7)+29=43\°[/tex]
By definition , the angle "V" ant the angle "W" are supplementary. Then:
[tex]\angle V+43\°=180[/tex]
Solving for the angle "V", we get:
[tex]\angle V=180\°-43\°=137\°[/tex]
2) It is important to remember that the diagonals of a parallelogram intersect each other at the half-way point. Then:
[tex]EA=EC[/tex]
Therefore, we can write the following equation:
[tex]8x-14=2(2x+11)[/tex]
Solving for "x" we get:
[tex]8x-14=4x+22\\\\8x-4x=22+14\\\\4x=36\\\\x=9[/tex]
