I thought that a parallelogram had to have 2 adjacent angles add up to 180. Can someone attach a drawing of this figure please?
OA is D.
Hey! I got D as an answer as well and I think I can explain it. I attached a drawing I created in Paint so hopefully that'll help too.
Here's how I broke it down:
-They gave two angles, the 30 (CBD) and 80 (BAD).
-I drew in the CBD angle to make it easier to visualize.
-In a parallelogram, when one line (BD) connects the two parallel lines (AD and BC), it creates congruent alternate interior angles (the 30s and the X's). Angles diagonal from eachother also congruent, which is how I got the other 80 (BCD). You can also see that CBA and ADC (the one in question) are also congruent since both of them equal X+30. So we just need to figure out what X is so we can add it to 30 to get the whole angle.
-All the angles inside a parallelogram are supposed to have a sum of 360. So if you take 360 and subtract all the known values (80, 80, 30, 30) you should get a difference of 140.
-Therefore the two remaing angles (the X's) should equal 140. If you set it up as 2x=140 and then divide it out, you'll see that X=70.
-Then X+30 becomes 70+30 which equals 100.
I hope my explanation helps.... and is right
Yay for 1st post!
GeoII-12.JPG [ 11.59 KiB | Viewed 944 times ]