Answer
$\theta = 104.48^{o}$
$\phi = 75.52$
c = 63.24
Work Step by Step
The following are the given values:
a = 40
b = 60
d = 80
Using the Law of Cosines, we can find $\theta$:
$cos(\theta) = \frac{40^{2} + 60^{2} - 80^{2}}{2(40)(60)}$
$\theta = 104.48^{o}$
Knowing that a parallelogram has $360^{o}$, we can find $\phi$:
$\frac{360 - (104.48)(2)}{2} = 75.52$
$\phi = 75.52$
Using the Law of Cosines, we can find c:
$c^{2} = 40^{2} + 60^{2} - 2(40)(60)cos(75.52^{o})$
c = 63.24
$\theta = 104.48^{o}$
$\phi = 75.52$
c = 63.24
