Question

2 opposite angles of a parallelogram are (3x-2) and (63-2x). find all the angles of parallelogram

Answer 1

3x-2 = 63-2x
5x = 65
x = 65/5 = 13

Opp. angle = 63 - 2 * 13 = 63 - 26 = 37
Sum of opp. angles = 37*2 = 74
360 - 74 = 286
Another angle = 286/2 = 143

All angles are -
37, 37, 143 & 143

Answer 2

given :
2 opposite angles of a parallelogram are (3x - 2) and (63 - 2x)
need to find out :
all angles of parallelogram 
solution :
according to properties of a parallelogram opposite angles are equal 
⇒ (3x - 2) = (63 - 2x) 
⇒ 3x + 2x = 63 + 2 
⇒ 5x = 65 
⇒ x = 65/5 
∴ x = 13° 
by substituting the value of x in (3x - 2) and (63 - 2x) 
(3x - 2) 
⇒ 3*13 - 2 
⇒ 39 - 2 
⇒ 37° 

 (63 - 2x) 
⇒ 63 - 2*13 
⇒ 63 - 26 
⇒ 37° 

⇒ let one of the other angle be x 
according to the properties of a parallelogram the opposite angle will be equal 
∴ the other angle will also be x  
By angle sum property of a quadrilateral = 
 x + x + 37° + 37° = 360° 
2x + 74° = 360°
2x = 360° - 74° 
2x = 286 
x = 286/2 
x = 143° 
--------------------------------------------------------------------------------------------
the first angle = 37°
the second angle = 37° 
the second angle = 143° 
the third angle = 143° 

check : 
37° + 37° + 143° + 143° = 360 
74° + 286° = 360° 
360° = 360° 

hence proved and all angles are given