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

2
by vmjvnz

2016-03-13T16:43:11+05:30
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
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2016-03-13T16:58:35+05:30
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
please mark as best I've even given the reasons for the calculation
and if any doubt then plz ask me :D