Question

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

Answer 1

Answer:

x = 18.5° , y = 37°

Step-by-step explanation:

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

Answer 2

Answer:

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

Step-by-step 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 $y$

$2y=180-90-16\\y=\frac{74}{2}\\ y=37\°$

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 $x$

$4x=180-16-90\\x=\frac{74}{4}\\ x=18.5$

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