Degree measure of multiple polygons I made this design on the Desmos calculator, and I was wondering what the quickest way was to find the degree measure of each individual angle. 
What I know so far:


*

*The measures of each of the angles of the pentagon are 108

*The measures of each of the angles of the rectangle are 90 

*The measure of the sector angle is 107.53

*The measure of the smaller angle of the rhombus is 35.53

*The measure of the larger angle of the rhombus is 144.47

*The measure of the largest angle of the triangle is 162

*The measure of the angle in the triangle opposite the smallest side is 5.8

*The measure of the last angle in the triangle is 14.6

*The measure the bottom left angle of the trapezoid is 57.4

*The measure of the top left angle of the trapezoid is 84.2

*The measure of the bottom right angle of the trapezoid is 104.1

*The measure of the top right angle of the trapezoid is 114.3


What I still need:


*

*Nothing left, this is now finished!


Thanks.
 A: If you know the coordinates of every point in your shape, you can find any angle using a combination of Pythagoras' theorem and the Cosine rule.
Let us say that you have the coordinates of 3 points: $A(a_1, a_2)$, $B(b_1, b_2)$, $C(c_1, c_2)$.
To find $\angle ACB$ you would do the following:
First, find the lengths of the 3 sides of $\triangle ABC$ using Pythagoras: $AB$, $BC$, $AC$.
$$AB=\sqrt{(a_1-b_1)^2+(a_2-b_2)^2}$$
$$BC=\sqrt{(b_1-c_1)^2+(b_2-c_2)^2}$$
$$AC=\sqrt{(a_1-c_1)^2+(a_2-c_2)^2}$$
Next you can use the Cosine rule to find the angle:
$$\cos(\angle ACB)={{AB}^2+{BC}^2-{AC}^2\over 2{AB}.{BC}}$$
Using this, the final formula you would obtain is:
$$\cos(\angle ACB)={{(a_1-b_1)^2+(a_2-b_2)^2}+{(b_1-c_1)^2+(b_2-c_2)^2}-{(a_1-c_1)^2-(a_2-c_2)^2}\over 2{\sqrt{(a_1-b_1)^2+(a_2-b_2)^2}}.{\sqrt{(b_1-c_1)^2+(b_2-c_2)^2}}}$$
$$\cos(\angle ACB)={b_1^2+b_2^2-a_1b_1-a_2b_2-b_1c_1-b_2c_2+a_1c_1+a_2c_2\over {\sqrt{(a_1-b_1)^2+(a_2-b_2)^2}}.{\sqrt{(b_1-c_1)^2+(b_2-c_2)^2}}}$$
although I would advise doing this in 4 steps as shown above rather than like this to avoid making mistakes.
For example, with the smallest angle of the rhombus, $\angle BED$, you know that the 3 points which create the angle are: $B(9.2, 5.6)$, $E(2, -6.2)$, $D(10, -6.2)$.
Now substitute $B$ for $A$, $E$ for $B$ and $D$ for $C$ in the above formula to find the angle.
