Question

find the values of x and y in the picture

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
For the smaller triangle, \(x = 26+33\)

Step2: Calculate the value of \(x\)

\(x=26 + 33=59\)

Step3: Use the angle - sum property of a triangle

In a right - angled triangle (the larger triangle with the right angle), the sum of angles is \(180^{\circ}\). Let's consider the triangle with angles \(x^{\circ}\), \(y^{\circ}\) and \(90^{\circ}\).
We know that \(x + y+90=180\). Since \(x = 59\), then \(y=180-(90 + 59)\)

Step4: Calculate the value of \(y\)

\(y=180-(90 + 59)=180 - 149=31\)

Answer:

\(x = 59\), \(y = 31\)