Question 474438: TWO OPPOSITE ANGLES OF PARLLELOGRAM ARE 3X-2 DEGREE & 50-X DEGREE.
FIND THE MEASUREMENT OF ALL ANGLES. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the opposite angles of a parallelogram are congruent.
this means that an angle of 3x - 2 is equal to an angle of 50 - x degrees.
your equation is:
3x - 2 = 50 - x
add x to both sides of this equation and add 2 to both sides of this equation to get:
4x = 52
divide both sides of this equation by 4 to get:
x = 52/4 = 13
your first angle is equal to 3x - 2 which is equal to 39 - 2 which is equal to 37.
your second angle is 50 - x which is equal to 50 - 13 which is equal to 37.
both angles are equal so you're good.
the adjacent angles in a parallelogram are supplementary.
your adjacent angles to these angles are therefore equal to 180 - 37 = 143 degrees each.
143 + 37 = 180 so they're supplementary.
the sum of the angles of a quadrilateral is equal to 360 degrees and 2 * 37 + 2 * 143 = 74 + 286 = 360 so we're good here too.
