Question

Find the value of x and y.

Answer 1

"Drawing not to scale" tells you that you shouldn't take the picture at face value. It's possible that $x^\circ$ is not 90º.

What we do know from the picture is that

• the angles BAD and CAD are congruent (indicated by the labeled arcs) with measure $y^\circ$, which means ...
• line segment AD bisects the angle BAC, and ...
• the sides AB and AC are congruent (with unknown length, call it $z$).

AD is congruent to itself. This means the two triangles BAD and CAD are congruent, since they form a side-angle-side pair. So it follows that

• both angles ABD and ACD have measure 47º, and ...
• both angles BDA and CDA have measure $x^\circ$.

But angles BDA and CDA are supplementary, so

$2x^\circ=180^\circ\implies\boxed{x=90}$

and it turns out your suspicion was correct after all. (Still, you should never assume things appear as they seem.)

Lastly, the interior angles of any triangle always sum to 180º in measure. This means

$x^\circ+y^\circ+47^\circ=180^\circ\implies\boxed{y=43}$.