Question

using algebra find the values of x and y. 24.

Explanation:

Step1: Use the property of isosceles triangle

Since the two sides are equal, the base angles are equal. The angle adjacent to \(x\) is \(40^{\circ}\). Using the exterior - angle property of a triangle, \(x = 40^{\circ}+ 90^{\circ}\) (the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles).

Step2: Calculate \(x\)

\(x=130^{\circ}\)

Step3: Use the angle - sum property of a triangle

In the right - angled triangle, the sum of angles is \(180^{\circ}\). We know one angle is \(90^{\circ}\) and the other non - right angle (related to the \(40^{\circ}\) angle) is \(40^{\circ}\). So, \(y + 90^{\circ}+40^{\circ}=180^{\circ}\), then \(y=180^{\circ}-(90^{\circ} + 40^{\circ})\)

Step4: Calculate \(y\)

\(y = 50^{\circ}\)

Answer:

\(x = 130^{\circ}\), \(y = 50^{\circ}\)