Question

find the values of x and y.
x =

y =

Explanation:

Step1: Find the value of \( y \)

In a right - angled triangle, the two non - right angles are complementary.
Since one angle is \( 40^{\circ} \) and the other non - right angle is \( y \), we have \( y+40^{\circ}=90^{\circ} \).
Subtracting \( 40^{\circ} \) from both sides gives \( y = 90^{\circ}-40^{\circ}=50^{\circ} \).

Step2: Find the value of \( x \)

The exterior angle \( x \) of a triangle is equal to the sum of the two non - adjacent interior angles.
Here, the two non - adjacent interior angles are \( 40^{\circ} \) and \( y = 50^{\circ} \).
So \( x=40^{\circ}+50^{\circ}=90^{\circ} \).

Answer:

\( x = 90\), \( y = 50 \)