Question

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

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(x = 40+90\).

Step2: Calculate the value of \(x\)

\(x=130\).

Step3: Use the property of right - angled triangles

In a right - angled triangle (the smaller right - angled triangle with angle \(y\)), the sum of angles is \(180^{\circ}\). We know one angle is \(90^{\circ}\) and another is \(40^{\circ}\). Using the formula \(y + 40+90=180\), we can rewrite it as \(y=180-(90 + 40)\).

Step4: Calculate the value of \(y\)

\(y = 50\).

Answer:

\(x = 130\), \(y = 50\)