Name: sonia

9th Student

i have this difficult question my student asked me today. Our whole class was discussing it. I am wondering what is the way to solve this problem? Given AB||CD; m<D = 116 AK bisects <DAB

a. Find the measures of <DAB, <KAB, <DKA

b. Is there enough information for you to conclude that <D adn <C are supplementary, or is there enough information needed?

   D	               C
   _____________K______   (there is a line supposed to be connecting 
  /	              /	         A and K )
 /	             /
/___________________/
A	                B

Since the lines AB and CD are parallel, angles CDA and DAE are equal, each with an angle measure of 116^o.

Since EAB is a line, angle DAB has measure 180^o - 116^o = 64^o. Hence angle KAB has measure 32^o. Since the measures of the three interior angles of a triangle sum to 180^o, you can find the measure of angle DKA.

There is nothing in the problem that specifies where B is except that it is on the line through A and parallel to DC and hence there is no requirement that <D adn <C are supplementary.