Question

18° x y 29°

Explanation:

Step1: Find the value of \(x\)

Since the figure is symmetric about the dashed line, and the sum of angles on a straight line formed by the dashed line and the side of the figure (considering the upper part). The angle adjacent to \(18^{\circ}\) (using the property of symmetry and angle - sum in a triangle - like part for the upper section). The angle \(x = 90^{\circ}\) (as the dashed line is a perpendicular bisector for the upper part of the symmetric figure).

Step2: Find the value of \(y\)

We know that the sum of angles in a triangle is \(180^{\circ}\). For the left - hand triangle (considering the part with \(y\), \(18^{\circ}\) and the angle from the lower part). The angle from the lower part (due to symmetry) is \(29^{\circ}\). Using the angle - sum property of a triangle \(y+18^{\circ}+29^{\circ}=90^{\circ}\) (because the dashed line is perpendicular, so the right - angle is \(90^{\circ}\)). Then \(y=90^{\circ}-(18^{\circ} + 29^{\circ})\) \(y = 43^{\circ}\)

Answer:

\(x = 90^{\circ}\), \(y=43^{\circ}\)