Question

solve for x and y
18°
29°
x =
y =

Explanation:

Step1: Use the property of perpendicular lines

Since the dashed line is the axis of symmetry of the kite - shaped figure, the two lines (the axis of symmetry and the dashed line) are perpendicular. So \(x = 90^{\circ}\).

Step2: Use the angle - sum property of a triangle

In the left - hand triangle, we know that the sum of angles in a triangle is \(180^{\circ}\). One angle is \(18^{\circ}\), another is \(90^{\circ}\), and let the third angle be \(y\). Also, using the fact that the axis of symmetry of the kite bisects the angles.
We know that \(y+18^{\circ}+90^{\circ}+29^{\circ}=180^{\circ}\) (sum of angles in the larger part of the figure considering the symmetry). But if we consider the right - angled triangle formed by \(x = 90^{\circ}\), \(18^{\circ}\) and \(y\) (by the property of the kite's symmetry).

$$y=180^{\circ}-(90^{\circ} + 29^{\circ})$$

$$y = 61^{\circ}$$

Answer:

\(x = 29^{\circ}\), \(y=61^{\circ}\)