Question

find the measures of the numbered angles in the kite shown to the right.
m∠1 = 90°, m∠2 = 53°, m∠3 = \square°

Explanation:

Step1: Use triangle angle sum

The triangle with ∠1, ∠2, and 37° is right-angled at ∠1. Sum of angles: $90^\circ + 53^\circ + 37^\circ = 180^\circ$ (checks out). The triangle with ∠1, ∠3, and ∠4 is congruent to the triangle with ∠1, ∠2, and 37° (kite has two pairs of congruent adjacent sides, diagonals intersect at right angles, and one diagonal bisects the other). Thus, the angle corresponding to 37° in the lower triangle is equal to ∠3.

Step2: Identify congruent angles

Since the triangles are congruent, ∠3 = 37°.

Answer:

37