Question

in the kite pictured above, find all the missing measures
angle 1 =
angle 2 =
cd =

Explanation:

Step1: Use the property of right - angle in kite

In a kite, the diagonals are perpendicular. So, \(\angle1 = 90^{\circ}\)

Step2: Use the angle - sum property of a right - triangle

In right - triangle \(ABC\), we know that the sum of angles in a triangle is \(180^{\circ}\). Given one angle is \(90^{\circ}\) and another angle (adjacent to \(51^{\circ}\)) is \(51^{\circ}\) (because of the property of kite: the diagonal bisects the vertex angles). For \(\angle2\), we use \(\angle2=90^{\circ}- 51^{\circ}\)

$$ \angle2 = 39^{\circ} $$

Step3: Use the property of congruent sides in kite

In a kite, two pairs of adjacent sides are equal. Since \(AD = 21\), and \(AD\) and \(CD\) are adjacent sides (by the property of kite: \(AD = CD\) when considering the non - overlapping pairs of adjacent sides)

$$ CD=21 $$

Answer:

Angle \(1 = 90^{\circ}\)
Angle \(2 = 39^{\circ}\)
\(CD = 21\)