Answer: ________________________________________________________ The measurements of the 2 (TWO) supplementary angles are: ________________________________________________________ 58° and 122° . ________________________________________________________ Explanation: _________________________________________________ Two supplementary angles: _________________________________________________ Angle 1: "x: _________________________________________________ Angle 2: "(6 + 2x)" _________________________________________________ All supplementary angles, by definition, add up to 180 degrees, so given that the 2 (two) angles are supplementary:
(x) + (6 + 2x) = 180 ; Find "x" and "(6 + 2x)" . __________________________________________________ x + 6 + 2x = 180 ;
3x + 6 = 180 ;
Subtract "6" from each side of the equation ; ___________________________________________________ 3x + 6 − 6 = 180 − 6 ;
3x = 174 ; ___________________________________________________ Divide each side of the equation by "3" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
3x / 3 = 172 / 3 ;
x = 58 ; ________________________________________________ So: ________________________________________________ Angle 1: "x" : x = 58 . ________________________________________________ Angle 2: "(6 + 2x)" = " 6 + 2(58) = 122 . ________________________________________________ 122 + 58 =? 180 ? Yes! ________________________________________________ So, the measurements of the 2 (TWO) supplementary angles are: 58° and 122° . ________________________________________________
I believe since the definition of perimeter is adding the lengths of all three sides of the angles the, width of the rectangle would be 5, and the length of the rectangle would be 10.
