Question

find the values of x and y.
(the figure is not drawn to scale.)
x = and y =

Explanation:

Step1: Recall angle - bisector and perpendicular - bisector properties

In the right - angled triangle formed inside the larger triangle, the angle bisector divides the non - right angle.

Step2: Calculate x

The non - right angle in the right - angled triangle is part of an isosceles triangle (indicated by the equal segments). The non - right angle of the right - angled triangle is half of the given angle. So, $x=\frac{52^{\circ}}{2}=26^{\circ}$.

Step3: Calculate y

In a right - angled triangle, the sum of the two non - right angles is $90^{\circ}$. Since one non - right angle is $x = 26^{\circ}$, then $y=90^{\circ}-x$. Substituting $x = 26^{\circ}$, we get $y = 90^{\circ}-26^{\circ}=64^{\circ}$.

Answer:

$x = 26$ and $y = 64$