The parallelogram and diagonal are drawn to scale here: 



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:

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


cos(A) = 

cos(A) = 

cos(A) = 

cos(A) = 

cos(A) = 

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