SOLUTION: ABCD is a parallelogram. AB=8 BC=10 and diagonal AC=13. determine the measure of angle BAD to the nearest minute

We use the Law of cosines to find ∠ABC



Chosse AC as the "THIRD SIDE"

AC² = AB² + BC² - 2·AB·BC·cos(∠ABC)

13² = 8² + 10² - 2·8·10·cos(∠ABC)
169 = 64 + 100 - 160·cos(∠ABC)
169 = 164 - 160·cos(∠ABC)
5 = -160·cos(∠ABC)
 = cos(∠ABC)
-0.03125 = cos(∠ABC)

So ∠ABC is an obtuse angle in the 
second quadrant. so we find the reference angle
by finding the inverse cosine of +0.03125 which is
88.20921534° and subtract from 180° and get 

∠ABC = 91.79078466°

Since two adjacent angles of a parallelogram are 
supplementary, we can find ∠BAD by subtracting ∠ABC 
from 180°.

But we'll just get 88.20921534° again which is the same as
the reference angle for ∠ABC.

Therefore ∠BAD = 88.20921534°

To get that to the nearest minute we multiply the
decimal part 0.20921534 by 60 getting 12.55229204
which rounds to 13 minutes.

Answer: ∠BAD = 88°13'

Edwin