Question

question
find the values of x and y

answer attempt 2 out of 5
x =

y =

Explanation:

Step1: Find the value of \(x\)

In a triangle, the exterior angle is equal to the sum of the two non - adjacent interior angles. Here, the triangle with the \(40^{\circ}\) angle has two equal sides (marked by the red lines), so the base angles are equal. The exterior angle \(x\) is twice the \(40^{\circ}\) angle.
\(x = 2\times40^{\circ}=80^{\circ}\)

Step2: Find the value of \(y\)

We know that one angle in the right - angled triangle is \(90^{\circ}\) and we can use the angle - sum property of a triangle (\(180^{\circ}\)).
\(y+90^{\circ}+40^{\circ}=180^{\circ}\)
\(y = 180^{\circ}-90^{\circ}-40^{\circ}=50^{\circ}\)

Answer:

\(x = 80\), \(y = 50\)