Question

find the values of x and y.
x = □
y = □

Explanation:

Step1: Use the property of right - angled triangle and the given angle

In a right - angled triangle, if one of the non - right angles is \(20^{\circ}\), and we know that \(x\) is complementary to \(20^{\circ}\) (because the line is perpendicular). So \(x = 25^{\circ}+20^{\circ}\) (using the exterior angle property of a triangle, the exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles).

$$x=45^{\circ}$$

Step2: Use the property of right - angled triangle for \(y\)

Since the triangle with angle \(y\) is a right - angled triangle and we know one of the non - right angles is \(x = 45^{\circ}\), then \(y=90^{\circ}-x\) (because the sum of angles in a right - angled triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\)).

$$y = 90^{\circ}-45^{\circ}=45^{\circ}$$

Answer:

\(x = 45\), \(y = 45\)