Question

find the measures of the numbered angles in the kite. 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. We already know $\angle1 = 90^{\circ}$. Also, a kite has one pair of non - congruent adjacent angles bisected by a diagonal.

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 ($\sum_{i = 1}^{3}\angle_{i}=180^{\circ}$), we have $\angle2=180^{\circ}-90^{\circ}-39^{\circ}$.

Step3: Calculate the value of $\angle2$

$180 - 90-39 = 51$.

Answer:

$51$