Question

For the parallelogram, if m<2+5x-28 abd m<4=3x-10, find m< 3. ...?

Answer 1

Opposite angles of a parallelogram are equal, so: 


5x - 28 = 3x - 10 

2x = 18 

x = 9 


Plug x = 9 into the equations 

m angle 2 = 5x - 28 = 5 * 9 - 28 = 17 

m angle 4 = 3x - 10 = 3 * 9 - 10 = 17 


The sum of all angles in a parallelogram is 360, 

and we know: m angle 1 = m angle 3, so: 

m angle 1 + m angle 2 + m angle 3 + m angle 4 = 360 

m angle 3 + 17 + m angle 3 + 17 = 360 

2 * (m angle 3) = 360 - 17 - 17 = 326 


m angle 3 = 163