Question 545828
<pre>
The parallelogram and diagonal are drawn to scale here: 

{{{drawing(400,2800/19,-3,16,-2,5,

line(0,0,8.3,0), line(8.3,0,14.172891566,3.472891566),
line(14.172891566,3.472891566,5.872891566,3.472891566),
line(5.872891566,3.472891566,0,0),green(line(5.872891566,3.472891566,8.3,0)),
locate(4,0,83),green(locate(7.2,2.3,42)), locate(2,2.3,68), locate(0,0,A),
locate(8.3,0,B), locate(5.8,4.3,D),locate(14.1,4.3,C) 



 )}}}

We have a case of side-side-side in triangle ABD, so we use 
the law of cosines solved for the cosine on triangle ABD:

<i>The cosine of any given angle equals the sum of the squares of 
its sides minus the square of its opposite side, divided by twice
the product of its sides</i>


cos(A) = {{{(AD^2+AB^2-BD^2)/(2*AD*AB)}}}

cos(A) = {{{(68^2+83^2-42^2)/(2*68*83)}}}

cos(A) = {{{(4624+6889-1764)/(11288)}}}

cos(A) = {{{(9749)/(11288)}}}

cos(A) = {{{(4624+6889-1764)/(11288)}}}

cos(A) = .86366052545

A = 30.26989518°

That's also the measure of angle C

Angles ABC and ADC are supplementary to angles A and C,
so their measures are:

180° - 30.26989518° = 149.7301048° each.

You can round off as you teacher told you, probably to
the nearst whole degree, which would be 30° and 150°.

Edwin</pre>