Final answer:
In a kite, the two angles opposite each other are congruent. The remaining angles of the kite add up to 180°.
Step-by-step explanation:
A kite has two pairs of congruent angles. Let's say one angle measures 27°. Since the opposite angle in a kite is congruent to the opposite angle, the other angle must also measure 27°. So, the two angles opposite each other in the kite are both 27°.
Now, the remaining angles in the kite must add up to 180°. We already know that the opposite angles each measure 27°, so the sum of the other two angles is 180° - (27° + 27°) = 126°. Since these two angles are congruent, each of them must measure 126° ÷ 2 = 63°.