Question

Question 6

8.2
#6
Quadrilateral LMQW is shown.
mL-14x-10
mM-231-4
mN-6x422
IF LMNW is a parallelogram, what is the value of y
Type your answer as a whole number,

Answer 1

Value of y is 6

Explanation:

Two features of a parallelogram:

1. Opposite angles are equal:

which means:
m∠L = m∠N

∴
`14x - 10 = 6x + 22`

Bring like terms together and make x the subject of the equation:

`14x - 6x = 22 + 10`

`8x = 32`

`x = (32)/(8)`

∴x = 4

Substitute this value of x to determine the measurement of ∠N:

m∠L =
`14(4) - 10`

= 46°

∴m∠N = 46°

2. Adjacent angles are supplementary:

which means:

m∠M + m∠N = 180°

`(23y - 4) + 46 = 180`

Expand the parenthesis, bring like terms together and make y the subject of the equation:

`23y - 4 + 46 = 180`

`23y = 180 - 46 + 4`

`23y = 138`

`y = (138)/(23)`

∴y = 6