Question

Lines

AB and
CD
are straight lines. Find x and y. Give reasons to justify your solutions.

Answer 1

x = 18.5° , y = 37°

Explanation:

In the picture, i hope that it's a clear solution.

Answer 2

The solutions are
`x=18.5\°` and
`y=37\°`

Explanation:

We know by given that

Lines AB and CD are straight lines. This means all angles formed on these lines must sum 180°.

So,
`16+90+2y=180` by defintion of straight line and suplementary angles.

Let's solve for
`y`

`2y=180-90-16\\y=(74)/(2)\\ y=37\°`

Then,
`\angle O = 16\°` by vertical angles defintion.

Now,
`90+4x+16=180`, by defintion of straight line and suplementary angles.

Let's solve for
`x`

`4x=180-16-90\\x=(74)/(4)\\ x=18.5`

Therefore, the solutions are
`x=18.5\°` and
`y=37\°`