Question

Find the values of x and y.
(10x – 4)º
16yº
(18y – 18)°
6(x + 2)°

Answer 1

The value of x is 4 and the value of y is 9

Explanation:

In the attached pictures we can see that two lines are intersecting with each other and four angles are form. The angles opposite to each other are also called vertical angles.

The opposite pairs of angles are:

(10x-4)° and 6(x+2)°

(18y-18)° and 16y°

When two lines intersect each other, the vertical angles formed are congruent(Can also be called equal in measurement)

So,

`10x-4=6(x+2)\\10x-4 = 6x+12`

Subtracting 6x from both sides

`10x-4-6x = 6x+12-6x\\4x-4 = 12`

Adding 4 on both sides

`4x-4+4 = 12+4\\4x = 16`

Dividing both sides by 4

`(4x)/(4) = (16)/(4)\\x = 4`

AND

`18y-18=16y`

Adding 18 on both sides

`18y-18+18 = 16y+18\\18y = 16y+18`

Subtracting 16y from both sides

`18y-16y = 16y+18-16y\\2y = 18`

Dividing both sides by 2

`(2y)/(2) = (18)/(2)\\y = 9`

Hence,

The value of x is 4 and the value of y is 9