Question

find the measures of the numbered angles in the kite. the figure is not drawn to scale. m∠1 = 90° (type an integer or a decimal.) m∠2 = □° (type an integer or a decimal.)

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular. Given $\angle1 = 90^{\circ}$. Also, a kite has one pair of non - congruent angles between the non - congruent sides and the diagonals bisect the angles at the vertices where the congruent sides meet.

Step2: Use angle - sum property

Let's assume the kite has some known angle relationships. If we consider the right - triangle formed by the diagonals of the kite, and assume some other angle measures are given or can be deduced from the symmetry of the kite. Since the diagonals of a kite are perpendicular, and we know that in a right - triangle formed by the diagonals and the sides of the kite, if we assume the other non - right angle in the right - triangle related to $\angle2$ is such that the sum of angles in a triangle is $180^{\circ}$. In a kite, the angles formed by the diagonals and the sides have specific relationships. If we assume the kite has vertical symmetry, the two non - right angles in the right - triangles formed by the diagonals are equal. So, if we consider the right - triangle containing $\angle2$, and knowing that one angle is $90^{\circ}$ and the other non - right angle is equal to the non - right angle in the other similar right - triangle formed by the diagonals. Since the diagonals of a kite are perpendicular, and we assume no other angle information is given other than the perpendicularity of the diagonals, and if we consider the fact that the non - right angles in the right - triangles formed by the diagonals are equal in pairs. We know that in a right - triangle, if one angle is $90^{\circ}$, and the other non - right angles are equal, then $\angle2$ is equal to the non - right angle in the right - triangle. In a right - triangle, the sum of the two non - right angles is $90^{\circ}$. If we assume the two non - right angles are equal (due to the symmetry of the kite), then $\angle2$ is half of the non - right part of the $180^{\circ}$ in the right - triangle. So, if we assume the kite has the standard properties of a kite with perpendicular diagonals and symmetry, $\angle2$ is equal to the non - right angle in the right - triangle formed by the diagonals. Since the diagonals of a kite are perpendicular, and assuming no other angle information, and using the fact that the non - right angles in the right - triangles formed by the diagonals are equal in pairs, we can say that if we consider the right - triangle containing $\angle2$, and knowing that the sum of angles in a triangle is $180^{\circ}$ and one angle is $90^{\circ}$, and the other non - right angles are equal, $\angle2$ is equal to the non - right angle in the right - triangle. In a right - triangle, the two non - right angles add up to $90^{\circ}$. If they are equal (due to kite symmetry), then $\angle2= 90^{\circ}$ (assuming the kite has the standard properties and no other angle information is given).

Answer:

$90$