Question

find the measures of the numbered angles in the kite.
the figure is not drawn to scale.
m∠1 = 51° (type an integer or a decimal.)

Explanation:

Step1: Recall kite - angle properties

In a kite, the diagonals are perpendicular. So, one of the angles formed by the diagonals is 90°. Also, in a kite, the non - vertex angles are bisected by the diagonal.

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

In the right - triangle formed, we know one of the non - right angles is 26°. In a right - triangle, the sum of the interior angles is 180°. Let the unknown angle be ∠1. We have the equation $m\angle1+26^{\circ}+90^{\circ}=180^{\circ}$.

Step3: Solve for ∠1

$m\angle1=180^{\circ}-(90^{\circ} + 26^{\circ})=180^{\circ}-116^{\circ}=64^{\circ}$

For ∠2, since the diagonals of a kite are perpendicular, $m\angle2 = 90^{\circ}$

Answer:

$m\angle1 = 64^{\circ}$, $m\angle2=90^{\circ}$