Question

solve for x and y

Explanation:

Step1: Use the property of right - angled triangles

In the upper triangle, since the two sides are equal (marked with the same symbol), the triangle is isosceles. The sum of angles in a triangle is \(180^{\circ}\). In the lower triangle, we know one angle is \(41^{\circ}\) and it is also isosceles. For the angle \(y\), in the lower isosceles triangle, \(y = 41^{\circ}\) (base angles of an isosceles triangle are equal).

Step2: Use the angle - sum property for the upper triangle

In the upper triangle, we know one angle is \(78^{\circ}\). Using the angle - sum property of a triangle (\(180^{\circ}\)), \(x=180^{\circ}- 2\times78^{\circ}\).

$$x = 180^{\circ}-156^{\circ}=24^{\circ}$$

Answer:

\(x = 24\), \(y = 41\)