If each quadrilateral below is a rectangle find the missing measure in #3
Accepted Solution
A:
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°