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° . ________________________________________________
The angle that the ramp makes with the ground is 11.54°
Step-by-step explanation:
From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.
We can use the fact that the sin(θ) = to find the angle that the ramp makes with the ground.
