Question

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

Explanation:

To determine the measure of angle \( \angle 1 \) in a kite, we use the property that the diagonals of a kite are perpendicular to each other. This means they intersect at right angles (90 degrees).

Step 1: Recall the property of a kite's diagonals

In a kite, one of the diagonals is the perpendicular bisector of the other, and they intersect at \( 90^\circ \). So, the angle formed by their intersection (which is \( \angle 1 \)) is a right angle.

Step 2: Determine the measure of \( \angle 1 \)

Since the diagonals of a kite are perpendicular, \( m\angle 1 = 90^\circ \).

Answer:

\( 90 \)