Question

If each quadrilateral below is a rectangle find the missing measure in #3

Answer 1

You can solve this exercise as below (View the figure attached):

 1.Divide the figure in four equals parts. Now we have 4 rectangles with the same dimensions.
 2.Choose the rectangle that has the angle given in the problem, which we will call "α" (α=59°). 
 3. We must remember that the sum of the internal angles of a triangle is 180°. We have α=59° and the right angle, so we can find the other one, which we will call "β1":
 β1=180°-90°-59° β1=31°
 4. As we can see in the figure, "α" is alternate interior with α1 (α=α1=59°) and β1 is alternate interior with m∠11 (β1=m∠11=31°).
 5. The others rectangles have the same dimensions of the rectangle we chose, so they have the same angles too.
 We can notice in the figure that m∠7+m∠8+m∠9+m∠10= 360°

 The answer is:
 m∠1=59°
 m∠2=31°
 m∠3=59°
 m∠4=31°
 m∠5=31°
 m∠6=59°
 m∠7=118°
 m∠8=62°
 m∠9=62°
 m∠10=118°
 m∠11=31°