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 diagonal properties

The diagonals of a kite are perpendicular, so $\angle 1 = 90^\circ$ (given, confirmed by property).

Step2: Analyze right triangle angles

In the right triangle containing the $20^\circ$ angle and $\angle 2$, the non-right angles sum to $90^\circ$.
$\text{Angle adjacent to } \angle 2 = 20^\circ$

Step3: Calculate $\angle 2$

$\angle 2 = 90^\circ - 20^\circ$

Answer:

$m\angle 1 = 90^\circ$
$m\angle 2 = 70^\circ$