finding linear pairs

Question

I have a shape that is a "X" shape.  The top middle area is #2, the area to the right is #3, the bottom area is #4 and the left area is #1.

 

I was suppose to identify all of the linear pairs using angle numbers.

This is what I have. ∠1 and ∠4, ∠4 and ∠3, ∠3 and ∠2, and ∠2 and ∠1.

 

 

Answer 1

You have the linear and vertical angle pairs correct.  Good job!

 

angle 1 = 4x + 12

angle 2 = 7x + 3

 

Since angles 1 and 2 are a linear pair, they add up to 180^o.  So add them up and solve for x:

 

angle 1 + angle 2 = 180^o

4x + 12 + 7x + 3 = 180^o

11x + 15 = 180^o

11x = 165^o

x = 15^o

 

Since x = 15, the measure of angle 1 is:

 

angle 1 = 4x + 12

angle 1 = 4*15 + 12

angle 1 = 60 + 12

angle 1 = 72^o

 

Angles 1 and 3 are vertical angles, so:

 

measure angle 1 = measure angle 3 = 72^o

Angle 3 = 6y

6y = 72^o

y = 12^o