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 - angle properties

In a kite, the diagonals are perpendicular. So, $\angle1 = 90^{\circ}$. Also, a kite has one pair of non - vertex angles that are congruent and the diagonal bisects the vertex angles.

Step2: Use angle - sum property of a triangle

In the right - triangle formed, one angle is $39^{\circ}$ and another is $90^{\circ}$. Let $\angle2$ be the third angle. By the angle - sum property of a triangle ($\sum\text{angles in a triangle}=180^{\circ}$), we have $m\angle2=180^{\circ}-(90^{\circ} + 39^{\circ})$.
$m\angle2=180^{\circ}-129^{\circ}=51^{\circ}$

Answer:

$m\angle2 = 51^{\circ}$