Question

find the measures of the numbered angles in the kite.
m∠1 = \square°

Explanation:

Step1: Find m∠3 first

In a kite, one diagonal bisects the vertex angle. So AC bisects ∠BAD. Given ∠BAD = 46°, then $m∠3 = \frac{46°}{2} = 23°$.

Step2: Analyze triangle ACD

AC ≅ AC (common side), AD ≅ AB, CD ≅ CB (kite properties), so △ACD ≅ △ACB. That means ∠1 is a right angle? Wait, no—diagonals of a kite are perpendicular. So AC ⊥ BD, so $m∠1 = 90°$.

Answer:

90