Another test question which seems so hard!

ABCD is a parallelogram in which ∠DAB=75° and ∠DBC=60° . Calculate the measures of the ∠CDB abd ∠ADB .

In the this question there was no figure given and just the question so thats why i havent given the figure too!

So pls can anyone explain this with the reason for the angles!

rosala Jul 7, 2014

#1**+5 **

It will be very useful if you draw your own picture for this. Start by drawing an arbitrary parallelogram. the letters ABCD must label the vertices in order either clockwise or counter clockwise. It does not matter which is which, but this essentially guarantees that A is opposite C and B is opposite D. Once you have this labeled you'll need segment DB in your picture so that you have angle DBC to label. Now label the angles you know. You know angle A=75 and C is opposite A. In parallelograms opposite angels are congruent so C=75 as well. Now we know two angles of that triangle because DBC is also in that triangle. We know triangles Sum to 180 so CDB=180-75-60=45

Angle ADB is alternate interior to DBC they are congruent, therefore ADB=60

jboy314 Jul 7, 2014

#2**+5 **

The angles as listed don't make sense....."B" would be located in two places!!!...Let's do this, rosala...let's list the "vertices' starting at the top left and going "clockwise" as.... ABCD.

So <DAB = 75 ....and the angle opposite this (BCD) is equal to it

Now <CDA = 60 .........and the angle opposite this (ABC) is equal to it

Remember that in a paralleogram, opposite angles are equal.....!!!

(I wish we had a diagram....it would make this question easier........Also, remember that in describing angles, that <ABC is just the same as <CBA..!!!)

I hope this helps!!!

CPhill Jul 7, 2014

#3**+5 **

jboy , thank you very much for your help!i still have some doubts but!umm!i couldnt understand properly how u found out CDB . i was thinking that as DBC is 60 then in a parallelogram opposite angles are congruent so why cant CDB also be 60 becoz it is also opposite!i have made the figure lots of time and have made one just now too and so the figure made me think this!

Is the figure made above correct!im not good at making such kinda things so i dont know what ull think about this!BTW on ∠CDB ive written 60 becoz i think its that as opposite angles are congruent!so what do u think about it!If you can then can u please explain me a lil further , maybe with ur diagram !

rosala Jul 7, 2014

#5**+10 **

Best Answer

CPhill i think urs and mine are both the same!becoz ive written also what u have said !opposite angles are equal!

rosala Jul 7, 2014

#6**+5 **

OK...I can work with your diagram, rosala

<ABC = <ADC = 60 and

<BAD = < DCB = 75

Remember that the opposite angles are equal (congruent) !!!

CPhill Jul 7, 2014

#8**0 **

Thanks, rosala..I think I've made the proper corrections......thanks for pointing out my mistake!!

CPhill Jul 7, 2014

#9**+5 **

actually i didnt liked pointing out ur mistake like this on the forum ! ill try to delete my post for that!BTW your welcome!

rosala Jul 7, 2014