Question

Solve for x and Y using the angles shown, please helppp

Answer 1

x = 6

y = 24

Explanation:

(14x + 4) + (16x - 4) <--- you add them because they are supplementary angles and are equal to 180°

(14x + 4) + (16x - 4) = 180

30x = 180

`(30x)/(30) = (180)/(30)`

x = 6

Then you plug in 6 to (14x + 4)

(14(6) + 4) = 84 + 4 = 88

180 - 88 = 92

Now subtract 92 from 180 and make it equal to (4y - 8) to get y.

(4y - 8) = 180 - 92 ---> (4y - 8) = 88

+ 8 + 8

4y = 96

`(4y)/(4) = (96)/(4)`

y = 24

Answer 2

x = 6, y = 24

Explanation:

We have the vertical angles and supplementary angles.

Vertical angles are congruent. Therefore we have the equation:

`(1)\qquad14x+4=4y-8`

Supplementary angles add up to 180°. Therefore we have the equation:

`(2)\qquad(16x-4)+(14x+4)=180`

Solve (2):

`(16x-4)+(14x+4)=180\qquad\text{combine like terms}\\(16x+14x)+(-4+4)=180\\30x=180\qquad\text{divide both sides by 30}\\x=6`

Put the value of x to (1) and sole:

`4y-8=14(6)+4\\4y-8=84+4\\4y-8=88\qquad\text{add 8 to both sides}\\4y=96\qquad\text{divide both sides by 4}\\y=24`