Question

Lines AB and CD intersect at E, mLAED = 110,

m_DEB = 3x + 2y, mZBEC = 9x + y, and mZCEA =
= 70.
Find the values of x and y. Check your answer. [Only an
algebraic solution will be accepted.]
А
'D
110°
(3x+2y)
70°
E
(9x + y)
с
B

Answer 1

x = 10, y = 20

Explanation:

Form a system of equations:

From the picture at the bottom you can see that vertical angles are equal, so:

`3x + 2y = 70`

Then, since the angles all together will add up to 360, you can do

`3x+2y+9x+y+70+9x+y=360`

`21x+4y+70=360`

subtract 70 from both sides

`21x + 4y = 290`

With the equation 3x + 2y = 70, multiply both sides by 2

`6x+4y=140`

Subtract the two equations:

`15x=150\\x=10`

Plug this into one of the original equations

`30+2y=70\\2y = 40\\y=20`

Answer 2

45,698,09864,58586,96403