Question

find the measures of the numbered angles in the kite shown to the right.

Explanation:

Step1: Recall Kite Properties

A kite has two distinct pairs of adjacent sides equal. The diagonals of a kite are perpendicular, so \(\angle1 = \angle3 = 90^\circ\). Also, one diagonal bisects the vertex angles and the other diagonal.

Step2: Find \(\angle2\) and \(\angle4\)

In the right triangle with angle \(46^\circ\), \(\angle2 = 90^\circ - 46^\circ = 44^\circ\). Since the diagonal bisects the angles, \(\angle4=\angle2 = 44^\circ\).

Step3: Find \(\angle5\)

\(\angle5 = 46^\circ\) (because the diagonal bisects the vertex angle).

Answer:

\(\angle1 = 90^\circ\), \(\angle2 = 44^\circ\), \(\angle3 = 90^\circ\), \(\angle4 = 44^\circ\), \(\angle5 = 46^\circ\)